A251132 Number of (n+1) X (3+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.

369, 1002, 1997, 4110, 8050, 15830, 30770, 60088, 117492, 230956, 455680, 902602, 1792830, 3569098, 7116086, 14203652, 28370704, 56695536, 113333908, 226597798, 453110314, 906118110, 1812113626, 3624082160, 7247993420, 14495787220

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*(369 - 1212*x + 782*x^2 + 1464*x^3 - 2514*x^4 + 1146*x^5 + 62*x^6 - 114*x^7 - 5*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

a(n) = (36*(-5+9*(-1)^n+9*2^(3+n)) + 202*n + 151*n^2 + 50*n^3 + 5*n^4) / 12 for n>3.

(End)

Example

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

Crossrefs

Column 3 of A251137.

Sequence in context: A062041 A373764 A205730 * A183351 A275170 A205911

Adjacent sequences: A251129 A251130 A251131 * A251133 A251134 A251135

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved