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A227165 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227165 #6 Jul 23 2025 05:34:53
%S A227165 2,3,3,4,8,4,5,18,18,5,6,36,62,36,6,7,66,193,193,66,7,8,113,558,944,
%T A227165 558,113,8,9,183,1507,4528,4528,1507,183,9,10,283,3828,20336,37012,
%U A227165 20336,3828,283,10,11,421,9149,85018,283430,283430,85018,9149,421,11,12,606
%N A227165 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
%C A227165 Table starts
%C A227165 ..2...3.....4.......5........6..........7............8............9
%C A227165 ..3...8....18......36.......66........113..........183..........283
%C A227165 ..4..18....62.....193......558.......1507.........3828.........9149
%C A227165 ..5..36...193.....944.....4528......20336........85018.......330949
%C A227165 ..6..66...558....4528....37012.....283430......2010569.....13174529
%C A227165 ..7.113..1507...20336...283430....3754497.....46389565....529521521
%C A227165 ..8.183..3828...85018..2010569...46389565...1009485843..20376855291
%C A227165 ..9.283..9149..330949.13174529..529521521..20376855291.732609096798
%C A227165 .10.421.20609.1200425.79606861.5548518625.377546087348
%H A227165 R. H. Hardin, <a href="/A227165/b227165.txt">Table of n, a(n) for n = 1..127</a>
%F A227165 Empirical for column k:
%F A227165 k=1: a(n) = n + 1
%F A227165 k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (23/24)*n^2 + (11/12)*n + 1
%F A227165 k=3: [polynomial of degree 9] for n>3
%F A227165 k=4: [polynomial of degree 19] for n>8
%F A227165 k=5: [polynomial of degree 39] for n>19
%e A227165 Some solutions for n=4 k=4
%e A227165 ..1..1..1..0....1..0..0..0....1..1..1..0....1..1..1..1....0..0..0..0
%e A227165 ..0..0..0..1....0..0..1..0....1..0..0..0....1..1..0..0....0..0..0..1
%e A227165 ..0..0..0..1....0..1..1..0....0..0..0..1....0..0..0..0....0..0..0..1
%e A227165 ..0..0..0..0....0..1..1..0....0..0..1..1....0..0..1..1....0..0..0..0
%K A227165 nonn,tabl
%O A227165 1,1
%A A227165 _R. H. Hardin_ Jul 03 2013