A251135 Number of (n+1) X (6+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.

4699, 9786, 15830, 27738, 46023, 79226, 135959, 240780, 434193, 804400, 1519053, 2920510, 5684595, 11169870, 22084427, 43851224, 87307005, 174131892, 347676817, 694650138, 1388459119, 2775924642, 5550678879, 11099992388, 22198396553

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*(4699 - 18408*x + 18201*x^2 + 12986*x^3 - 35970*x^4 + 22238*x^5 - 2915*x^6 - 1012*x^7 + 39*x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 - 2*x)).

a(n) = (9*(3271+441*(-1)^n+441*2^(1+n)) + 15178*n + 4111*n^2 + 578*n^3 + 35*n^4) / 12 for n>3.

(End)

Example

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

Crossrefs

Column 6 of A251137.

Sequence in context: A256808 A114542 A114568 * A237699 A235022 A223246

Adjacent sequences: A251132 A251133 A251134 * A251136 A251137 A251138

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved