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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A176772 A109408 A292714 * A017535 A180693 A013799

Adjacent sequences:  A202456 A202457 A202458 * A202460 A202461 A202462

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 19 2011

STATUS

approved

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Last modified January 23 03:08 EST 2019. Contains 319370 sequences. (Running on oeis4.)