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%I #4 Mar 06 2016 20:07:30
%S 0,6,6,60,432,60,450,11280,11280,450,3000,250992,943488,250992,3000,
%T 18750,5125008,68182800,68182800,5125008,18750,112500,99482544,
%U 4546948272,16086672048,4546948272,99482544,112500,656250,1867222224
%N T(n,k)=Number of nXk 0..5 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling five exactly once.
%C Table starts
%C ......0..........6.............60................450...................3000
%C ......6........432..........11280.............250992................5125008
%C .....60......11280.........943488...........68182800.............4546948272
%C ....450.....250992.......68182800........16086672048..........3515869538472
%C ...3000....5125008.....4546948272......3515869538472.......2524680110862912
%C ..18750...99482544...288987039048....733651366146384....1733054018904626400
%C .112500.1867222224.17784013336560.148379658813705408.1153865935196746139616
%H R. H. Hardin, <a href="/A269888/b269888.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 10*a(n-1) -25*a(n-2)
%F k=2: a(n) = 30*a(n-1) -197*a(n-2) -420*a(n-3) -196*a(n-4) for n>5
%F k=3: [order 10] for n>11
%F k=4: [order 28] for n>29
%e Some solutions for n=2 k=4
%e ..3..2..0..2. .3..0..2..5. .3..0..4..5. .3..0..1..5. .0..4..2..3
%e ..0..0..0..4. .2..0..1..1. .1..4..4..4. .1..0..0..1. .4..4..0..1
%Y Column 1 is A269760.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 06 2016
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