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A250427 Number of (n+1)X(3+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.

%I A250427 #8 Jul 23 2025 12:23:52
%S A250427 81,324,1296,3600,10000,22500,50625,99225,194481,345744,614656,
%T A250427 1016064,1679616,2624400,4100625,6125625,9150625,13176900,18974736,
%U A250427 26501904,37015056,50381604,68574961,91298025,121550625,158760000,207360000
%N A250427 Number of (n+1)X(3+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
%C A250427 Column 3 of A250432
%H A250427 R. H. Hardin, <a href="/A250427/b250427.txt">Table of n, a(n) for n = 1..210</a>
%F A250427 Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16)
%F A250427 Empirical for n mod 2 = 0: a(n) = (1/4096)*n^8 + (1/128)*n^7 + (55/512)*n^6 + (53/64)*n^5 + (1001/256)*n^4 + (185/16)*n^3 + (167/8)*n^2 + 21*n + 9
%F A250427 Empirical for n mod 2 = 1: a(n) = (1/4096)*n^8 + (1/128)*n^7 + (111/1024)*n^6 + (109/128)*n^5 + (8483/2048)*n^4 + (1635/128)*n^3 + (24975/1024)*n^2 + (3375/128)*n + (50625/4096).
%F A250427 a(n+1) = A202094(n). - _R. J. Mathar_, Dec 04 2014
%e A250427 Some solutions for n=6
%e A250427 ..0..0..0..0....0..0..0..1....0..0..1..1....0..0..0..0....0..0..1..0
%e A250427 ..0..0..1..1....0..0..0..0....0..0..1..0....0..0..0..1....0..0..1..0
%e A250427 ..0..0..1..0....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
%e A250427 ..0..0..1..1....0..0..0..1....0..0..1..0....0..0..0..1....1..0..1..0
%e A250427 ..0..0..1..1....0..0..1..1....0..1..1..1....0..0..1..1....0..0..1..1
%e A250427 ..1..0..1..1....0..0..1..1....1..0..1..0....0..0..0..1....1..0..1..0
%e A250427 ..1..0..1..1....1..1..1..1....0..1..1..1....0..1..1..1....1..1..1..1
%K A250427 nonn
%O A250427 1,1
%A A250427 _R. H. Hardin_, Nov 22 2014