a(n)~c*(sqrt(5)+1)^n,其中c=(sqert(5)+3)/10。
显然,一个数组的n=4行在n X n板上以k步数行走,从一个角开始,每一步到<=4个相邻方块中的一个:
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,
1,2,6,16,48,128,384,1024,3072,8192,24576,65536,196608,
1,2,6,18,58,186,602,1946,6298,20378,65946,213402,690586,
1,2,6,18,60,198,684,2322,8100,27702,96876,331938,1161540,
1,2,6,18,60,200,698,2432,8658,30762,110374,395428,1422916,
1,2,6,18,60,200,700,2448,8800,31552,115104,418176,1537536,
1,2,6,18,60,200,700,2450,8818,31730,116182,425172,1573416,
1,2,6,18,60,200,700,2450,8820,31750,116400,426600,1583400,
1,2,6,18,60,200,700,2450,8820,31752,116422,426862,1585246,
1,2,6,18,60,200,700,2450,8820,31752,116424,426886,1585556,
1,2,6,18,60,200,700,2450,8820,31752,116424,426888,1585582,
(结束)
将4X4板上长度=n的车行分解为4宽走廊中独立的垂直和水平步行组合,导致斐波那契数的指数卷积,参见。A052899号. [大卫·斯卡布勒2010年10月17日]