cp's OEIS Frontend

A250726 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%I A250726 #7 Nov 16 2018 07:51:17
%S A250726 257,596,1158,2092,3605,6016,9728,15297,23407,34943,50970,72810,
%T A250726 102025,140498,190420,254375,335331,436729,562478,717048,905469,
%U A250726 1133428,1407272,1734109,2121815,2579139,3115714,3742166,4470129,5312358,6282748,7396451
%N A250726 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H A250726 R. H. Hardin, <a href="/A250726/b250726.txt">Table of n, a(n) for n = 1..210</a>
%F A250726 Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>10.
%F A250726 Empirical for n mod 2 = 0: a(n) = (1/360)*n^6 + (1/12)*n^5 + (49/36)*n^4 + (13/3)*n^3 + (15169/360)*n^2 + (1957/12)*n + 43 for n>2.
%F A250726 Empirical for n mod 2 = 1: a(n) = (1/360)*n^6 + (1/12)*n^5 + (49/36)*n^4 + (13/3)*n^3 + (15169/360)*n^2 + (1957/12)*n + 40 for n>2.
%F A250726 Empirical g.f.: x*(257 - 946*x + 1180*x^2 - 110*x^3 - 1079*x^4 + 1060*x^5 - 440*x^6 + 93*x^7 - 12*x^8 + x^9) / ((1 - x)^7*(1 + x)). - _Colin Barker_, Nov 16 2018
%e A250726 Some solutions for n=4:
%e A250726 ..0..0..0..0..0..0....0..0..0..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1
%e A250726 ..0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1
%e A250726 ..0..0..0..0..0..0....0..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..1..1
%e A250726 ..0..0..0..0..0..1....0..1..1..1..1..1....0..0..0..0..0..0....0..1..0..0..1..1
%e A250726 ..0..0..0..0..0..1....1..1..1..1..1..1....1..1..1..0..1..0....1..0..1..0..1..1
%Y A250726 Column 5 of A250729.
%K A250726 nonn
%O A250726 1,1
%A A250726 _R. H. Hardin_, Nov 27 2014