A184546 Number of (n+2) X 9 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

539, 1513, 3461, 7307, 14767, 28844, 54543, 99872, 177207, 305112, 510719, 832788, 1325583, 2063717, 3148137, 4713439, 6936723, 10048219, 14343937, 20200617, 28093279, 38615698, 52504155, 70664842, 94205327, 124470514, 163083563

Offset

1,1

Comments

Column 7 of A184548.

Links

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

Formula

Empirical: a(n) = (1/362880)*n^9 + (1/5760)*n^8 + (289/60480)*n^7 + (217/2880)*n^6 + (12949/17280)*n^5 + (28049/5760)*n^4 + (468401/22680)*n^3 + (210319/1440)*n^2 + (145955/504)*n + 77.

Conjectures from Colin Barker, Apr 14 2018: (Start)

G.f.: x*(539 - 3877*x + 12586*x^2 - 23898*x^3 + 29072*x^4 - 23429*x^5 + 12502*x^6 - 4270*x^7 + 853*x^8 - 77*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

Some solutions for 4 X 9:
..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0..0
..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1..1
..0..0..0..0..0..0..0..0..0....0..0..1..1..1..1..1..0..1
..1..1..1..1..1..1..1..1..1....0..0..1..1..1..1..1..1..0

Crossrefs

Cf. A184548.

Sequence in context: A111258 A239347 A118630 * A252386 A289221 A345390

Adjacent sequences: A184543 A184544 A184545 * A184547 A184548 A184549

Keyword

nonn

Author

R. H. Hardin, Jan 16 2011

Status

approved