cp's OEIS Frontend

A250658 Number of (4+1) X (n+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 A250658 #7 Nov 15 2018 14:58:15
%S A250658 79,142,221,316,427,554,697,856,1031,1222,1429,1652,1891,2146,2417,
%T A250658 2704,3007,3326,3661,4012,4379,4762,5161,5576,6007,6454,6917,7396,
%U A250658 7891,8402,8929,9472,10031,10606,11197,11804,12427,13066,13721,14392,15079,15782
%N A250658 Number of (4+1) X (n+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 A250658 R. H. Hardin, <a href="/A250658/b250658.txt">Table of n, a(n) for n = 1..210</a>
%F A250658 Empirical: a(n) = 8*n^2 + 39*n + 32.
%F A250658 Conjectures from _Colin Barker_, Nov 15 2018: (Start)
%F A250658 G.f.: x*(79 - 95*x + 32*x^2) / (1 - x)^3.
%F A250658 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250658 (End)
%e A250658 Some solutions for n=4:
%e A250658 ..1..1..1..1..1....0..0..0..0..0....1..1..1..0..0....1..1..1..0..0
%e A250658 ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
%e A250658 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..1....0..0..0..0..0
%e A250658 ..1..1..1..1..1....0..0..0..0..0....0..0..0..0..1....0..1..1..1..1
%e A250658 ..0..1..1..1..1....0..0..0..0..0....0..0..0..0..1....0..1..1..1..1
%Y A250658 Row 4 of A250656.
%K A250658 nonn
%O A250658 1,1
%A A250658 _R. H. Hardin_, Nov 26 2014