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A269097 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

%I A269097 #4 Feb 19 2016 09:52:09
%S A269097 0,4,4,24,96,24,108,1152,1152,108,432,11424,31296,11424,432,1620,
%T A269097 103488,715320,715320,103488,1620,5832,889056,15024096,37963968,
%U A269097 15024096,889056,5832,20412,7375872,300056400,1856325000,1856325000,300056400,7375872
%N A269097 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.
%C A269097 Table starts
%C A269097 ......0..........4.............24................108....................432
%C A269097 ......4.........96...........1152..............11424.................103488
%C A269097 .....24.......1152..........31296.............715320...............15024096
%C A269097 ....108......11424.........715320...........37963968.............1856325000
%C A269097 ....432.....103488.......15024096.........1856325000...........211625837280
%C A269097 ...1620.....889056......300056400........86415197088.........22984646281176
%C A269097 ...5832....7375872.....5795398368......3892946216856.......2416707037884480
%C A269097 ..20412...59698464...109294975080....171307237216320.....248267055360211392
%C A269097 ..69984..474360768..2024660774592...7406621052177000...25062609875880382656
%C A269097 .236196.3715826016.36988673403168.315868041326151072.2495854741014485439624
%H A269097 R. H. Hardin, <a href="/A269097/b269097.txt">Table of n, a(n) for n = 1..264</a>
%F A269097 Empirical for column k:
%F A269097 k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F A269097 k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
%F A269097 k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>5
%F A269097 k=4: [order 6] for n>7
%F A269097 k=5: [order 14] for n>15
%F A269097 k=6: [order 26] for n>27
%F A269097 k=7: [order 64] for n>65
%e A269097 Some solutions for n=3 k=4
%e A269097 ..0..1..3..2. .0..0..2..2. .2..2..2..3. .0..2..2..0. .0..0..1..1
%e A269097 ..0..3..1..0. .0..2..3..3. .0..2..2..2. .0..2..0..0. .0..2..0..0
%e A269097 ..0..2..3..2. .1..1..1..3. .2..0..0..3. .0..2..3..2. .2..2..1..1
%Y A269097 Column 1 is A120908.
%K A269097 nonn,tabl
%O A269097 1,2
%A A269097 _R. H. Hardin_, Feb 19 2016