A251136 Number of (n+1) X (7+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.

10033, 19548, 30770, 51679, 82431, 135959, 223663, 380641, 662361, 1191797, 2199909, 4160395, 8005403, 15610747, 30712547, 60794301, 120807237, 240664809, 480177897, 958978999, 1916316823, 3830699263, 7659125559, 15315604409

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>10.

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

G.f.: x*(10033 - 40650*x + 43911*x^2 + 20853*x^3 - 73278*x^4 + 48222*x^5 - 7753*x^6 - 1661*x^7 + 61*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

a(n) = (68472 + 6724*(-1)^n + 1369*2^(3+n) + 34882*n + 8827*n^2 + 1130*n^3 + 65*n^4) / 12 for n>3.

(End)

Example

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

Crossrefs

Column 7 of A251137.

Sequence in context: A241880 A245209 A205822 * A213318 A346026 A097648

Adjacent sequences: A251133 A251134 A251135 * A251137 A251138 A251139

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved