cp's OEIS Frontend

A250779 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%I A250779 #8 Nov 19 2018 09:14:03
%S A250779 99,238,534,1152,2426,5028,10306,20960,42394,85420,171666,344392,
%T A250779 690122,1381908,2765858,5534192,11071354,22146236,44296626,88598104,
%U A250779 177201834,354410148,708827714,1417663872,2835337306,5670685388,11341382866
%N A250779 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%H A250779 R. H. Hardin, <a href="/A250779/b250779.txt">Table of n, a(n) for n = 1..210</a>
%F A250779 Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).
%F A250779 Conjectures from _Colin Barker_, Nov 19 2018: (Start)
%F A250779 G.f.: x*(99 - 356*x + 492*x^2 - 304*x^3 + 73*x^4) / ((1 - x)^4*(1 - 2*x)).
%F A250779 a(n) = (-288 + 507*2^n - 116*n - 12*n^2 - 4*n^3) / 6.
%F A250779 (End)
%e A250779 Some solutions for n=4:
%e A250779 ..1..0..1..0..0....0..1..0..0..1....1..0..1..0..0....0..0..1..0..0
%e A250779 ..1..0..1..0..1....0..1..0..0..1....1..0..1..0..0....0..0..1..0..1
%e A250779 ..1..1..0..1..0....0..1..0..0..1....1..0..1..0..0....1..1..0..1..0
%e A250779 ..1..1..1..0..1....0..1..0..0..1....1..0..1..1..1....1..1..0..1..0
%e A250779 ..1..1..1..1..0....1..0..1..1..0....1..0..1..1..1....1..1..1..0..1
%Y A250779 Column 4 of A250783.
%K A250779 nonn
%O A250779 1,1
%A A250779 _R. H. Hardin_, Nov 27 2014