A202459 Number of (n+2) X 8 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

2197, 5854, 14586, 33468, 71088, 141192, 264822, 473031, 810265, 1338508, 2142292, 3334680, 5064336, 7523802, 10959108, 15680847, 22076853, 30626626, 41917654, 56663788, 75725832, 100134516, 131116026, 170120271, 218852073, 279305472

Offset

1,1

Comments

Column 6 of A202461.

Links

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

Formula

Empirical: a(n) = (1/6720)*n^8 + (19/1680)*n^7 + (431/1440)*n^6 + (193/48)*n^5 + (90001/2880)*n^4 + (5873/40)*n^3 + (2076229/5040)*n^2 + (10915/14)*n + 823.

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

G.f.: x*(2197 - 13919*x + 40992*x^2 - 71610*x^3 + 80058*x^4 - 58194*x^5 + 26730*x^6 - 7071*x^7 + 823*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

Some solutions for n=4:
..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1
..0..0..0..0..0..1..1..1....0..0..0..0..0..1..0..0....0..0..0..0..0..1..1..1
..0..0..0..0..0..1..1..1....0..0..0..0..0..1..1..0....0..0..0..0..1..1..1..1
..0..1..1..1..1..1..1..1....0..0..0..0..1..1..1..1....0..0..1..1..1..1..1..1
..0..0..0..0..1..1..1..1....0..0..0..0..0..1..1..1....0..0..0..0..0..1..1..1

Crossrefs

Cf. A202461.

Sequence in context: A229319 A109408 A292714 * A017535 A180693 A013799

Adjacent sequences: A202456 A202457 A202458 * A202460 A202461 A202462

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved