A202456 Number of (n+2) X 5 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

1000, 1876, 3362, 5735, 9338, 14586, 21972, 32073, 45556, 63184, 85822, 114443, 150134, 194102, 247680, 312333, 389664, 481420, 589498, 715951, 862994, 1033010, 1228556, 1452369, 1707372, 1996680, 2323606, 2691667, 3104590, 3566318, 4081016

Offset

1,1

Comments

Column 3 of A202461.

Links

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

Formula

Empirical: a(n) = (1/20)*n^5 + 2*n^4 + (275/12)*n^3 + 113*n^2 + (10351/30)*n + 517.

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

G.f.: x*(1000 - 4124*x + 7106*x^2 - 6297*x^3 + 2838*x^4 - 517*x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A202461.

Sequence in context: A004266 A004267 A319441 * A168650 A043491 A100988

Adjacent sequences: A202453 A202454 A202455 * A202457 A202458 A202459

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved