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%I #26 Nov 29 2024 17:33:25
%S 1,4,0,9,12,0,16,40,24,0,25,84,160,24,0,36,144,408,496,0,0,49,220,768,
%T 1764,1208,0,0,64,312,1240,3768,6712,2240,0,0,81,420,1824,6508,17280,
%U 22672,2984,0,0,100,544,2520,9984,32520,74072,68272,2384,0,0,121,684
%N Array read by antidiagonals: T(n,k) is the number of n-step king's tours on a k X k board summed over all starting positions.
%H R. H. Hardin, <a href="/A186861/b186861.txt">Table of n, a(n) for n = 1..145</a>
%F Empirical, for all rows: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3,3,3,5,6,7,8,9 respectively for row=1..8.
%e Table starts:
%e 1 4 9 16 25 36 49 64 81 100
%e 0 12 40 84 144 220 312 420 544 684
%e 0 24 160 408 768 1240 1824 2520 3328 4248
%e 0 24 496 1764 3768 6508 9984 14196 19144 24828
%e 0 0 1208 6712 17280 32520 52432 77016 106272 140200
%e 0 0 2240 22672 74072 156484 268048 408764 578632 777652
%e 0 0 2984 68272 296360 722384 1335984 2129440 3102752 4255920
%e 0 0 2384 183472 1110000 3193800 6481216 10899404 16418600 23038804
%e 0 0 784 436984 3908376 13530576 30543072 54738536 85743256
%e 0 0 0 905776 12956800 55056168 139775784
%e Some n=3 solutions for 3 X 3:
%e 3 2 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 1 0
%e 1 0 0 1 0 0 0 2 0 1 2 0 2 3 0 0 2 0 2 0 0
%e 0 0 0 2 3 0 0 0 1 3 0 0 0 1 0 0 0 3 0 3 0
%Y Rows are A000290, A033586(n-1), A186862, A186863, A186864, A186865, A186866, A186867, A366829.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 27 2011