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A269214 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

%I A269214 #4 Feb 20 2016 11:29:48
%S A269214 0,4,0,24,96,0,108,768,1152,0,432,6528,18048,11424,0,1620,49536,
%T A269214 308544,361728,103488,0,5832,360960,4744704,12548544,6712704,889056,0,
%U A269214 20412,2546304,70371048,394072704,474091776,118872576,7375872,0,69984,17563392
%N A269214 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.
%C A269214 Table starts
%C A269214 .0........4..........24............108...............432................1620
%C A269214 .0.......96.........768...........6528.............49536..............360960
%C A269214 .0.....1152.......18048.........308544...........4744704............70371048
%C A269214 .0....11424......361728.......12548544.........394072704.........11985002256
%C A269214 .0...103488.....6712704......474091776.......30541426560.......1910809190712
%C A269214 .0...889056...118872576....17118725376.....2267772823680.....292321215814512
%C A269214 .0..7375872..2039727744...599456856000...163535201141376...43468685827935816
%C A269214 .0.59698464.34214296320.20531285093184.11544796423498368.6331185189881558208
%H A269214 R. H. Hardin, <a href="/A269214/b269214.txt">Table of n, a(n) for n = 1..161</a>
%F A269214 Empirical for column k:
%F A269214 k=1: a(n) = a(n-1)
%F A269214 k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
%F A269214 k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5
%F A269214 k=4: [order 6] for n>7
%F A269214 k=5: [order 20] for n>21
%F A269214 k=6: [order 42] for n>43
%F A269214 Empirical for row n:
%F A269214 n=1: a(n) = 6*a(n-1) -9*a(n-2)
%F A269214 n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)
%F A269214 n=3: [order 8]
%F A269214 n=4: [order 20]
%F A269214 n=5: [order 52] for n>53
%e A269214 Some solutions for n=3 k=4
%e A269214 ..2..2..3..2. .2..2..2..3. .0..1..0..2. .0..0..0..2. .2..2..0..0
%e A269214 ..0..2..0..2. .0..0..1..0. .1..1..3..0. .0..1..2..0. .0..0..2..3
%e A269214 ..2..1..0..1. .0..1..0..1. .0..1..0..2. .0..0..0..0. .0..0..1..3
%Y A269214 Column 2 is A269091.
%Y A269214 Row 1 is A120908.
%K A269214 nonn,tabl
%O A269214 1,2
%A A269214 _R. H. Hardin_, Feb 20 2016