A202458 Number of (n+2) X 7 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

1728, 4137, 9338, 19614, 38478, 71088, 124740, 209445, 338596, 529731, 805398, 1194128, 1731522, 2461458, 3437424, 4723983, 6398376, 8552269, 11293650, 14748882, 19064918, 24411684, 30984636, 39007497, 48735180, 60456903, 74499502

Offset

1,1

Comments

Column 5 of A202461.

Links

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

Formula

Empirical: a(n) = (1/840)*n^7 + (3/40)*n^6 + (47/30)*n^5 + 16*n^4 + (10847/120)*n^3 + (11557/40)*n^2 + (258737/420)*n + 715.

Conjectures from Colin Barker, May 31 2018: (Start)

G.f.: x*(1728 - 9687*x + 24626*x^2 - 36022*x^3 + 32318*x^4 - 17650*x^5 + 5408*x^6 - 715*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=4:
..0..0..0..0..1..1..0....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..0....0..0..0..0..0..0..0
..0..0..0..1..1..1..1....0..0..0..0..1..1..1....0..0..0..0..0..0..0
..0..0..0..1..1..1..1....1..1..1..1..1..1..1....0..0..0..0..1..1..0
..0..0..1..1..1..1..1....1..1..1..1..1..1..1....0..0..1..1..1..1..1
..0..0..0..1..1..1..1....0..0..1..1..1..1..1....0..1..1..1..1..1..1

Crossrefs

Cf. A202461.

Sequence in context: A305494 A032354 A305475 * A179694 A202200 A251188

Adjacent sequences: A202455 A202456 A202457 * A202459 A202460 A202461

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved