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A202329 Number of (n+1)X(n+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

%I A202329 #14 Jul 22 2025 16:32:42
%S A202329 16,48,162,576,2102,7790,29174,110112,418134,1595622,6113746,23505358,
%T A202329 90633802,350351642,1357278302,5268292832,20483876822,79765662902,
%U A202329 311038321442,1214362277702,4746455801882,18570960418922,72728638093802
%N A202329 Number of (n+1)X(n+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
%C A202329 Diagonal of A202335
%H A202329 R. H. Hardin, <a href="/A202329/b202329.txt">Table of n, a(n) for n = 1..71</a>
%F A202329 Empirical: (n+1)*(27*n-40)*a(n) = (135*n^2-123*n-100)*a(n-1) - 2*(54*n^2-63*n-10)*a(n-2) - 8*(2*n-5)*a(n-3). - _Vaclav Kotesovec_, Oct 19 2012
%F A202329 Another recurrence (empirical): (n+1)*(9*n^2-19*n+8)*a(n) = (45*n^3-68*n^2-13*n+20)*a(n-1) - 2*(2*n-3)*(9*n^2-n-2)*a(n-2). - _Vaclav Kotesovec_, Oct 26 2012
%e A202329 Some solutions for n=5
%e A202329 ..0..0..0..0..0..1....0..0..0..0..1..0....0..0..0..0..1..0....0..0..0..0..0..1
%e A202329 ..0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..1..0....0..0..0..0..0..1
%e A202329 ..0..0..0..0..0..1....0..0..0..0..1..1....0..0..1..1..1..1....0..0..0..0..0..1
%e A202329 ..0..0..0..0..0..1....0..0..1..1..1..1....0..0..1..1..1..1....0..0..0..0..1..1
%e A202329 ..0..0..0..1..1..1....0..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
%e A202329 ..0..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1....1..1..1..1..1..1
%K A202329 nonn
%O A202329 1,1
%A A202329 _R. H. Hardin_ Dec 17 2011