A202455 Number of (n+2) X 4 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

729, 1194, 1876, 2835, 4137, 5854, 8064, 10851, 14305, 18522, 23604, 29659, 36801, 45150, 54832, 65979, 78729, 93226, 109620, 128067, 148729, 171774, 197376, 225715, 256977, 291354, 329044, 370251, 415185, 464062, 517104, 574539, 636601, 703530

Offset

1,1

Comments

Column 2 of A202461.

Links

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

Formula

Empirical: a(n) = (1/4)*n^4 + (15/2)*n^3 + (229/4)*n^2 + 237*n + 427.

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

G.f.: x*(729 - 2451*x + 3196*x^2 - 1895*x^3 + 427*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A202461.

Sequence in context: A045791 A088035 A054259 * A046319 A119710 A043455

Adjacent sequences: A202452 A202453 A202454 * A202456 A202457 A202458

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved