A251133 Number of (n+1) X (4+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.

919, 2264, 4110, 8008, 14753, 27738, 51679, 97758, 186223, 359276, 699161, 1372028, 2707973, 5368806, 10675899, 21273570, 42448163, 84773896, 169396869, 338610768, 677000585, 1353737746, 2707162679, 5413957638, 10827484663, 21654469188

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*(919 - 3250*x + 2473*x^2 + 3590*x^3 - 7100*x^4 + 3770*x^5 - 165*x^6 - 290*x^7 + 7*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

a(n) = (3063 + 961*(-1)^n + 121*2^(5+n) + 1726*n + 691*n^2 + 146*n^3 + 11*n^4) / 12 for n>3.

(End)

Example

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

Crossrefs

Column 4 of A251137.

Sequence in context: A084843 A059668 A162870 * A083142 A332191 A068163

Adjacent sequences: A251130 A251131 A251132 * A251134 A251135 A251136

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved