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.

81, 270, 746, 1796, 3896, 7790, 14588, 25885, 43903, 71658, 113154, 173606, 259694, 379850, 544580, 766823, 1062349, 1450198, 1953162, 2598312, 3417572, 4448342, 5734172, 7325489, 9280379, 11665426, 14556610, 18040266, 22214106, 27188306

Offset: 1

Author

R. H. Hardin, Dec 17 2011

Keywords

• nonn

Comments

Column 6 of A202335.

Examples

			Some solutions for n=5:
..0..0..0..0..0..1..1....0..0..0..0..0..1..0....0..0..0..0..0..0..0
..0..0..0..0..1..1..1....0..0..0..0..1..1..1....0..0..0..0..0..0..0
..0..0..0..0..1..1..1....0..0..1..1..1..1..1....0..0..0..0..0..0..1
..0..0..0..0..1..1..1....0..0..1..1..1..1..1....0..0..0..0..0..0..1
..0..0..0..1..1..1..1....1..1..1..1..1..1..1....0..0..0..0..0..1..1
..0..0..0..0..1..1..1....0..1..1..1..1..1..1....0..0..0..1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A202335.

Formula

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.

Conjectures from Colin Barker, May 28 2018: (Start)

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.

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.

(End)