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A232023 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

%I A232023 #6 Jul 23 2025 06:48:18
%S A232023 3,3,9,9,22,27,22,66,121,81,51,212,852,704,243,121,716,6443,11517,
%T A232023 4059,729,292,2447,52680,196196,156913,23422,2187,704,8312,429976,
%U A232023 3668759,6129361,2125749,135166,6561,1691,28118,3466702,66962048,266779524
%N A232023 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.
%C A232023 Table starts
%C A232023 .....3.......3..........9............22...............51.................121
%C A232023 .....9......22.........66...........212..............716................2447
%C A232023 ....27.....121........852..........6443............52680..............429976
%C A232023 ....81.....704......11517........196196..........3668759............66962048
%C A232023 ...243....4059.....156913.......6129361........266779524.........11145921002
%C A232023 ...729...23422....2125749.....189686855......19227454407.......1843879894941
%C A232023 ..2187..135166...28852936....5882557816....1386576216443.....304550219824247
%C A232023 ..6561..779977..391447970..182394008292..100026008988909...50342644960736903
%C A232023 .19683.4500958.5311170384.5654881014985.7214505515214571.8320423932674561675
%H A232023 R. H. Hardin, <a href="/A232023/b232023.txt">Table of n, a(n) for n = 1..262</a>
%F A232023 Empirical for column k:
%F A232023 k=1: a(n) = 3*a(n-1)
%F A232023 k=2: a(n) = 3*a(n-1) +13*a(n-2) +16*a(n-3) +7*a(n-4) +a(n-5)
%F A232023 k=3: [order 7] for n>8
%F A232023 k=4: [order 18] for n>19
%F A232023 k=5: [order 41] for n>42
%F A232023 k=6: [order 79] for n>81
%F A232023 Empirical for row n:
%F A232023 n=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 A232023 n=2: [order 17] for n>18
%F A232023 n=3: [order 61] for n>64
%e A232023 Some solutions for n=4 k=4
%e A232023 ..0..0..0..0....2..0..0..0....0..0..0..0....2..0..0..1....0..0..0..1
%e A232023 ..2..0..0..1....0..2..2..2....2..2..1..2....0..0..0..2....0..0..0..0
%e A232023 ..0..0..0..0....0..0..1..2....0..0..0..2....2..0..0..0....2..2..0..0
%e A232023 ..1..0..0..0....0..1..1..1....0..0..0..0....2..0..0..0....0..0..1..1
%Y A232023 Column 1 is A000244
%Y A232023 Row 1 is A202882 for n>1
%K A232023 nonn,tabl
%O A232023 1,1
%A A232023 _R. H. Hardin_, Nov 17 2013