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%I #4 Mar 04 2016 12:11:09
%S 0,6,6,60,480,60,450,17520,17520,450,3000,524160,2624640,524160,3000,
%T 18750,14288400,326697720,326697720,14288400,18750,112500,368958240,
%U 37212131520,170119348800,37212131520,368958240,112500,656250,9195061680
%N T(n,k)=Number of nXk 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.
%C Table starts
%C .....0.........6............60...............450..................3000
%C .....6.......480.........17520............524160..............14288400
%C ....60.....17520.......2624640.........326697720...........37212131520
%C ...450....524160.....326697720......170119348800........81208264293720
%C ..3000..14288400...37212131520....81208264293720....162622227315688800
%C .18750.368958240.4022791852800.36821411380183680.309460647800786666280
%H R. H. Hardin, <a href="/A269767/b269767.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 10*a(n-1) -25*a(n-2)
%F k=2: a(n) = 42*a(n-1) -441*a(n-2) for n>3
%F k=3: a(n) = 184*a(n-1) -9134*a(n-2) +61640*a(n-3) -112225*a(n-4) for n>5
%F k=4: [order 6] for n>7
%F k=5: [order 14] for n>15
%F k=6: [order 26] for n>27
%F k=7: [order 64] for n>65
%e Some solutions for n=2 k=4
%e ..0..5..3..4. .0..0..2..1. .3..5..1..2. .0..0..5..2. .3..1..2..4
%e ..0..2..5..4. .1..2..4..4. .3..3..0..5. .0..2..2..0. .3..2..2..0
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 04 2016
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