A253230 Number of (n+1) X (7+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

6740, 9551, 6231, 8216, 11022, 15363, 22656, 35736, 60273, 107607, 200418, 384066, 749271, 1477473, 2931552, 5837268, 11646141, 23261211, 46488558, 92940342, 185840883, 371638821, 743231436, 1486413288, 2972773497, 5945490303

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

Conjectures from Colin Barker, Dec 11 2018: (Start)

G.f.: x*(6740 - 24149*x + 19136*x^2 + 15840*x^3 - 27356*x^4 + 9682*x^5 - 11*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

a(n) = (3/32)*(25728 + 945*2^n + 9200*n + 624*n^2) for n>4.

(End)

Example

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

Crossrefs

Column 7 of A253231.

Sequence in context: A257486 A345591 A345849 * A253349 A253356 A204615

Adjacent sequences: A253227 A253228 A253229 * A253231 A253232 A253233

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved