A202332 Number of (n+1) X 6 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

64, 191, 478, 1052, 2102, 3896, 6800, 11299, 18020, 27757, 41498, 60454, 86090, 120158, 164732, 222245, 295528, 387851, 502966, 645152, 819262, 1030772, 1285832, 1591319, 1954892, 2385049, 2891186, 3483658, 4173842, 4974202, 5898356, 6961145

Offset

1,1

Comments

Column 5 of A202335.

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 + (1/12)*n^5 + (17/18)*n^4 + (16/3)*n^3 + (5779/360)*n^2 + (295/12)*n + 17.

Conjectures from Colin Barker, May 28 2018: (Start)

G.f.: x*(64 - 257*x + 485*x^2 - 523*x^3 + 331*x^4 - 115*x^5 + 17*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=5:
..0..0..0..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0
..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..1..0....0..0..0..0..1..0
..1..1..1..1..1..1....0..0..0..0..0..1....0..0..0..1..1..1....0..0..0..0..1..1
..1..1..1..1..1..1....0..0..0..0..0..1....1..1..1..1..1..1....0..0..0..0..1..1
..1..1..1..1..1..1....0..0..0..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....0..0..1..1..1..1

Crossrefs

Cf. A202335.

Sequence in context: A317763 A318342 A318074 * A208636 A135270 A045052

Adjacent sequences: A202329 A202330 A202331 * A202333 A202334 A202335

Keyword

nonn

Author

R. H. Hardin, Dec 17 2011

Status

approved