砌砖墙的趣题

王守恩

谢谢mathe！有您这4个数垫底。答案错不了。就是不知道怎么把这4个数合并了？

已知W(15,3)=138, W(15,8)=17878, W(15,18)=653517380, W(14,28)=W(15,28)=25564099775312=25563287029398+275875000+536870912+2。

W(15,1)=12+9+5+2=28,
W(15,2)=30+16+8+2=56,
W(15,3)=86+30+20+2=138,
W(15,4)=242+56+32+2=332,
W(15,5)=702+106+80+2=890,
W(15,6)=2006+200+128+2=1096,
W(15,7)=5798+380+320+2=2828,
W(15,8)=16644+720+512+2=6932,
W(15,9)=48006+1370+1280+2,
W(15,10)=138054+2600+2048+2,
W(15,11)=397806+4950+5120+2,
W(15,12)=1144834+9400+8192+2,
W(15,13)=3297478+17900+20480+2,
W(15,14)=9492606+34000+32768+2,
W(15,15)=27336652+64750+81920+2,
W(15,16)=78705382+123000+131072+2,
W(15,17)=226636566+234250+327680+2,
W(15,18)=652548090+445000+524288+2=653517380,

{30, 86, 242, 702, 2006, 5798, 16644, 48006, 138054, 397806, 1144834, 3297478, 9492606, 27336652, 78705382, 226636566, 652548090,
1878985062, 5410230726, 15578307566, 44855627780, 129157230942, 371892292214, 1070823293702, 3083308792698, 8878041313446, 25563287029398, 73606577835660, 211941644114254, 610261735551094}

LinearRecurrence[{3, 3, -11, 3, 3, -1}, {54, 22, 10, 6, 6, 12, 30}, 30]

{9, 16, 30, 56, 106, 200, 380, 720, 1370, 2600, 4950, 9400, 17900, 34000, 64750, 123000, 234250, 445000,
847500, 1610000, 3066250, 5825000, 11093750, 21075000, 40137500, 76250000, 145218750, 275875000, 525406250, 998125000, 1900937500}

LinearRecurrence[{0, 5, 0, -5}, {16, 30, 56, 106}, 30]

{5, 8, 20, 32, 80, 128, 320, 512, 1280, 2048, 5120, 8192, 20480, 32768, 81920, 131072, 327680, 524288, 1310720, 2097152, 5242880, 8388608, 20971520, 33554432, 83886080, 134217728, 335544320,536870912,1342177280,2147483648}

LinearRecurrence[{0, 4}, {2, 5}, 30]