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

1,1

Comments

Column 6 of A202335.

Links

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

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)

Example

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

Crossrefs

Cf. A202335.

Sequence in context: A237234 A237227 A206094 * A207042 A206087 A236809

Adjacent sequences: A202330 A202331 A202332 * A202334 A202335 A202336

Keyword

nonn

Author

R. H. Hardin, Dec 17 2011

Status

approved