50个1，50个2，50个3可组成多少种相邻数位都不相同的数
帖子由n个1，m个2，k个3可组成多少种相邻数位都不相同的数？northwolves 指出找不到简单的公式。
那么，能否编程计算出n=m=k=50的结果？
或者给10分钟时间能计算到多大的n？（n=m=k） n=1-9:
6
30
174
1092
7188
48852
339720
2403588
17236524 n a(n,n,n)
1 6
2 30
3 174
4 1092
5 7188
6 48852
7 339720
8 2403588
9 17236524
10 124948668
11 913820460
12 6732898800
13 49918950240
14 372104853600
15 2786716100592
16 20955408717396
17 158149624268220
18 1197390368733804
19 9091866006950892
20 69214297980023256
A110706 Number of linear arrangements of n blue, n red and n green items such that there are no adjacent items of the same color. 7
6, 30, 174, 1092, 7188, 48852, 339720, 2403588, 17236524, 124948668, 913820460, 6732898800, 49918950240, 372104853600, 2786716100592, 20955408717396, 158149624268220, 1197390368733804, 9091866006950892, 69214297980023256 (list; graph; listen; history; internal format)
OFFSET
1,1
COMMENTS
The number of circular arrangements is given by A110707 and A110710.
FORMULA
a(n) = 2 *( Sum] binomial(n-1, k) * ( binomial(n-1, k)*binomial(2n+1-2k, n+1) + binomial(n-1, k+1)*binomial(2n-2k, n+1)) )
PROG
(PARI) a(n)=2*sum(k=0, n\2, binomial(n-1, k)*(binomial(n-1, k)*binomial(2*n+1-2*k, n+1)+binomial(n-1, k+1)*binomial(2*n-2*k, n+1)))
CROSSREFS
Cf. A110707, A110710.
Sequence in context: A026331 A135490 A175925 * A001341 A089896 A057754
Adjacent sequences:A110703 A110704 A110705 * A110707 A110708 A110709
KEYWORD
nonn
AUTHOR
Max Alekseyev (maxale(AT)gmail.com), Aug 04 2005 (00:02) gp > for(i=1,100,print("a(",i,")=",a(i)))
a(1)=6
a(2)=30
a(3)=174
a(4)=1092
a(5)=7188
a(6)=48852
a(7)=339720
a(8)=2403588
a(9)=17236524
a(10)=124948668
a(11)=913820460
a(12)=6732898800
a(13)=49918950240
a(14)=372104853600
a(15)=2786716100592
a(16)=20955408717396
a(17)=158149624268220
a(18)=1197390368733804
a(19)=9091866006950892
a(20)=69214297980023256
a(21)=528150412279712856
a(22)=4038744418776845400
a(23)=30944390624047065984
a(24)=237516699913494859872
a(25)=1826086013748254354208
a(26)=14060749765349707607712
a(27)=108419462768852853411360
a(28)=837093723433477717410048
a(29)=6470979121569898636819584
a(30)=50079488713677575202500736
a(31)=387982401816883700210450784
a(32)=3008830071902513451691172340
a(33)=23355578609725312573413915996
a(34)=181454222489643445523121055308
a(35)=1410929075530217028966809771436
a(36)=10979559944932052584082034521160
a(37)=85504296448497664597176138172200
a(38)=666342090836575342810869307529640
a(39)=5196335866734293020072581291205680
a(40)=40548366159334986692251519592601144
a(41)=316600984318396358474067788054034792
a(42)=2473440399385321384181863105104711240
a(43)=19334338888097872133851929530263756008
a(44)=151211589346113407153873155612750437984
a(45)=1183201226095769143646013094593076929792
a(46)=9262761619343186896823542620683814327552
a(47)=72547402980720379307408101513774534473600
a(48)=568452882815731546922765274196011792412128
a(49)=4456054722123240923861790762275029981470624
a(50)=34944809867704420868762968362778850357165088
a(51)=274147371430665747033390016677581958159958560
a(52)=2151534123458342115664855183404876911768980800
a(53)=16891531014474743854827700730868265556544402240
a(54)=132660194992052638969652508875883676718351833920
a(55)=1042215716008997256156556500064910970795266407680
a(56)=8190582645372677718998263559678002957579518625920
a(57)=64388345049275795566012972006592224213972237987200
a(58)=506326155840395399722070165469770926974502777284480
a(59)=3982719132441830391958025714413424756984142532295040
a(60)=31336538308967379514657708421332661699444650175354880
a(61)=246626868347757426733648905645916297821821733669542400
a(62)=1941529484597800619620248555166987497423747232503360000
a(63)=15288265189039516569579953426135402450770672610746257600
a(64)=120414723092796156935730610443933392848561703471173154100
a(65)=948647469431830568173953387333513442924745469058124773020
a(66)=7475338284326073560709171028209634311725556165278385051660
a(67)=58918893989724828620259792011383097301935575680480059846700
a(68)=464486600168276476971060123234819703628399405372867807196840
a(69)=3662553007163831949948326207614139638295516036436782087893320
a(70)=28885783174772649638034285754252706807977228804193305563113160
a(71)=227861713323275822155965738601048793309733827940033202353666960
a(72)=1797807312928206882515923413338087340692159834272372424654277000
a(73)=14187216205357558899322140119941032318527100791446969198944436440
a(74)=111977630558250899351453851787690802535568466334635043570192828920
a(75)=883981694886194045915099682978724755614353746303013399314869204952
a(76)=6979609676484784779479286235526006893666327628653965268501081655136
a(77)=55117930081516616868772910479943869742814147606953974962324217730880
a(78)=435338093826904809506215082651967273805639376712008719095049713716544
a(79)=3438987775396227121017816949360617135314057290266529095422080019278752
a(80)=27170837832636974615809398863308843280350611707989242703275162872569368
a(81)=214705010694294097833729941669857415117829959725904643678957359285996232
a(82)=1696861732732598717138290444049715998410003925078107246379541728900386920
a(83)=13412640714774197250337848310466022807751108601087060377932407112815164008
a(84)=10603376350259707306709715822098819259989299189016291626860126019063786478
4
a(85)=83836792323606489665785221064655941533008759275410813321703672657330088020
8
a(86)=66295540572673231614558833865752795559799380789683434958940866976668909095
20
a(87)=52431442525072731993565189299456507022786176356512807970395232311875922531
200
a(88)=41472079493310195901973064849076649199251001405042627330139796160505775660
9280
a(89)=32807645684770679406571228177130201850370139117963559592814297812692232811
25120
a(90)=25956632124000022572974848787440766003997376665426522840048123984998670521
371392
a(91)=20538771112619686524406639425444805447852564799934190976359151824771269915
9211776
a(92)=16253700710456333429237496479021633753647588331978107934974387097161960850
56235520
a(93)=12864136589743950878360274144667404126747571476330915085443335432211631708
401921024
a(94)=10182596467765213807262897746550247534910696147121275685418734605997891907
6633725952
a(95)=80609251683143174591143075467859123926434751235828567714159073429907999014
1953446656
a(96)=63820279759174533659960335415845615245758520514652669772954583696231719150
48013353696
a(97)=50533455746072892090831361168063647414851515211097794702053168753099768300
933633725600
a(98)=40017027661016197999968124142437310845597536838521254446457074856188078489
9515255661344
a(99)=31692410443796524399433430052506862667502430439101916683254414842724153372
85300766955552
a(100)=2510206447012118942233591574635838380954104797212707759731753805266535970
4475946419493056
(00:02) gp > 回复楼上：
能否解释一下公式的意义：
a(n) = 2 *( Sum] binomial(n-1, k) * ( binomial(n-1, k)*binomial(2n+1-2k, n+1) + binomial(n-1, k+1)*binomial(2n-2k, n+1)) )
----------------------------------------------------------
我算得的结果：n从1到18，结果相同，但n>18，都不相同，我算得的略小。
f(19,19,19)=9091864886599260
f(20,20,20)=69214252708323576
f(50,50,50)=34914786015865910415118221775722841668386016 northwolves 的结果是对的。
我的递推公式，没错：
f(x,y,z)=g(x,y,z)+g(x,z,y)+g(y,z,x)
g(x,y,z)=f(x,y,z-1)-g(x,y,z-1)
g(x,y,z)表示最后一个数等于确定数（z代表的那个数）时的总个数
f(x,y,z)表示所要求的总个数
g(x,x,0)=2
g(x+1,x,0)=1
g(x,y,0)=0 ( x-y>1)
---------------------------
但是大数计算程序出了问题。
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