cp's OEIS Frontend

A202333 Number of (n+1) X 7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

%I A202333 #8 May 28 2018 08:09:49
%S A202333 81,270,746,1796,3896,7790,14588,25885,43903,71658,113154,173606,
%T A202333 259694,379850,544580,766823,1062349,1450198,1953162,2598312,3417572,
%U A202333 4448342,5734172,7325489,9280379,11665426,14556610,18040266,22214106,27188306
%N A202333 Number of (n+1) X 7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
%C A202333 Column 6 of A202335.
%H A202333 R. H. Hardin, <a href="/A202333/b202333.txt">Table of n, a(n) for n = 1..210</a>
%F A202333 Empirical: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (167/720)*n^5 + (265/144)*n^4 + (5999/720)*n^3 + (974/45)*n^2 + (4191/140)*n + 19.
%F A202333 Conjectures from _Colin Barker_, May 28 2018: (Start)
%F A202333 G.f.: x*(81 - 378*x + 854*x^2 - 1148*x^3 + 966*x^4 - 502*x^5 + 148*x^6 - 19*x^7) / (1 - x)^8.
%F A202333 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A202333 (End)
%e A202333 Some solutions for n=5:
%e A202333 ..0..0..0..0..0..1..1....0..0..0..0..0..1..0....0..0..0..0..0..0..0
%e A202333 ..0..0..0..0..1..1..1....0..0..0..0..1..1..1....0..0..0..0..0..0..0
%e A202333 ..0..0..0..0..1..1..1....0..0..1..1..1..1..1....0..0..0..0..0..0..1
%e A202333 ..0..0..0..0..1..1..1....0..0..1..1..1..1..1....0..0..0..0..0..0..1
%e A202333 ..0..0..0..1..1..1..1....1..1..1..1..1..1..1....0..0..0..0..0..1..1
%e A202333 ..0..0..0..0..1..1..1....0..1..1..1..1..1..1....0..0..0..1..1..1..1
%Y A202333 Cf. A202335.
%K A202333 nonn
%O A202333 1,1
%A A202333 _R. H. Hardin_, Dec 17 2011