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A231651 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

%I A231651 #6 Jul 23 2025 06:36:28
%S A231651 3,3,3,9,35,9,22,104,104,22,51,341,920,341,51,121,1189,7682,7682,1189,
%T A231651 121,292,4040,61574,137961,61574,4040,292,704,13560,490760,2412274,
%U A231651 2412274,490760,13560,704,1691,45803,3929027,42882766,96014413,42882766
%N A231651 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and vertical neighbors.
%C A231651 Table starts
%C A231651 ....3......3..........9............22................51..................121
%C A231651 ....3.....35........104...........341..............1189.................4040
%C A231651 ....9....104........920..........7682.............61574...............490760
%C A231651 ...22....341.......7682........137961...........2412274.............42882766
%C A231651 ...51...1189......61574.......2412274..........96014413...........3936913977
%C A231651 ..121...4040.....490760......42882766........3936913977.........374409597564
%C A231651 ..292..13560....3929027.....765163605......161357952814.......35384751611050
%C A231651 ..704..45803...31501117...13643499478.....6602715583511.....3335789961947404
%C A231651 .1691.155131..252454167..243317286312...270337779895196...314852421269523851
%C A231651 .4059.524683.2022844426.4340128403053.11069019817530645.29721381118553717447
%H A231651 R. H. Hardin, <a href="/A231651/b231651.txt">Table of n, a(n) for n = 1..161</a>
%F A231651 Empirical for column k:
%F A231651 k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
%F A231651 k=2: [order 11] for n>12
%F A231651 k=3: [order 36] for n>37
%e A231651 Some solutions for n=3 k=4
%e A231651 ..0..0..0..0....0..0..0..0....0..0..2..2....2..1..1..2....2..2..0..0
%e A231651 ..1..1..1..1....0..0..2..2....0..0..0..1....2..1..1..2....2..0..0..0
%e A231651 ..1..1..2..2....2..0..0..0....0..2..0..0....1..1..1..2....0..0..1..0
%Y A231651 Column 1 is A202882 for n>1
%K A231651 nonn,tabl
%O A231651 1,1
%A A231651 _R. H. Hardin_, Nov 12 2013