A202331 Number of (n+1) X 5 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

49, 129, 289, 576, 1052, 1796, 2906, 4501, 6723, 9739, 13743, 18958, 25638, 34070, 44576, 57515, 73285, 92325, 115117, 142188, 174112, 211512, 255062, 305489, 363575, 430159, 506139, 592474, 690186, 800362, 924156, 1062791, 1217561

Offset

1,1

Comments

Column 4 of A202335.

Links

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

Formula

Empirical: a(n) = (1/60)*n^5 + (3/8)*n^4 + 3*n^3 + (89/8)*n^2 + (1169/60)*n + 15.

Conjectures from Colin Barker, May 27 2018: (Start)

G.f.: x*(49 - 165*x + 250*x^2 - 203*x^3 + 86*x^4 - 15*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=5:
..0..0..0..0..0....0..0..0..0..0....0..0..0..1..0....0..0..0..0..0
..0..0..0..1..0....0..0..0..0..0....0..0..0..1..0....0..0..0..0..0
..0..0..0..1..0....0..0..0..0..0....0..0..0..1..1....0..0..0..1..0
..0..0..0..1..0....0..0..0..1..1....0..0..0..1..1....0..0..1..1..1
..0..1..1..1..1....0..0..0..1..1....1..1..1..1..1....1..1..1..1..1
..0..0..0..1..1....0..0..1..1..1....0..0..1..1..1....1..1..1..1..1

Crossrefs

Cf. A202335.

Sequence in context: A167718 A080665 A130007 * A044300 A044681 A250311

Adjacent sequences: A202328 A202329 A202330 * A202332 A202333 A202334

Keyword

nonn

Author

R. H. Hardin, Dec 17 2011

Status

approved