A184543 Number of (n+2) X 6 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

220, 537, 1048, 1837, 3024, 4774, 7307, 10909, 15944, 22867, 32238, 44737, 61180, 82536, 109945, 144737, 188452, 242861, 309988, 392133, 491896, 612202, 756327, 927925, 1131056, 1370215, 1650362, 1976953, 2355972, 2793964, 3298069, 3876057

Offset

1,1

Comments

Column 4 of A184548.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = (1/720)*n^6 + (11/240)*n^5 + (89/144)*n^4 + (209/48)*n^3 + (18317/360)*n^2 + (1231/10)*n + 41.

Conjectures from Colin Barker, Apr 13 2018: (Start)

G.f.: x*(220 - 1003*x + 1909*x^2 - 1922*x^3 + 1078*x^4 - 322*x^5 + 41*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 4 X 6:
..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..1
..0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..0..1
..0..0..0..0..1..1....0..0..0..1..1..0....0..0..0..1..0..0....1..1..1..1..1..0
..0..1..1..1..1..0....1..1..1..1..1..0....1..1..1..1..1..1....1..1..1..1..1..0

Crossrefs

Cf. A184548.

Sequence in context: A157107 A175738 A260203 * A234558 A211816 A135807

Adjacent sequences: A184540 A184541 A184542 * A184544 A184545 A184546

Keyword

nonn

Author

R. H. Hardin, Jan 16 2011

Status

approved