A251131 Number of (n+1) X (2+1) 0..2 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

133, 416, 1002, 2264, 4786, 9786, 19548, 38674, 76196, 150192, 296626, 587420, 1166206, 2320222, 4623712, 9225118, 18421072, 36804772, 73562342, 147065944, 294059610, 588031298, 1175956612, 2351786634, 4703423196, 9406669816

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 13*a(n-2) + 10*a(n-3) + 5*a(n-4) - 14*a(n-5) + 9*a(n-6) - 2*a(n-7) for n>9.

Conjectures from Colin Barker, Nov 26 2018: (Start)

G.f.: x*(133 - 382*x + 235*x^2 + 330*x^3 - 597*x^4 + 264*x^5 + 27*x^6 - 26*x^7 - 4*x^8) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

a(n) = (-873 + 49*(-1)^n + 841*2^(1+n) - 614*n - 11*n^2 + 38*n^3 + 5*n^4) / 12 for n>2.

(End)

Example

Some solutions for n=4:
..1..1..1....0..0..2....0..1..2....0..0..2....0..0..1....0..0..2....0..1..2
..0..0..0....1..0..2....1..0..0....2..0..2....0..0..1....0..0..0....0..0..0
..1..1..1....2..0..2....1..0..0....2..0..2....1..1..1....0..0..0....1..0..0
..1..0..0....2..0..2....2..0..0....2..0..1....0..0..0....0..0..0....1..0..0
..2..0..0....2..0..1....2..0..0....2..0..0....0..0..0....2..1..1....1..0..0

Crossrefs

Column 2 of A251137.

Sequence in context: A259638 A070158 A055940 * A267288 A334037 A137879

Adjacent sequences: A251128 A251129 A251130 * A251132 A251133 A251134

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved