A206259 Number of (n+1) X (n+1) 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.

16, 28, 78, 260, 932, 3440, 12878, 48628, 184764, 705440, 2704164, 10400608, 40116608, 155117528, 601080398, 2333606228, 9075135308, 35345263808, 137846528828, 538257874448, 2104098963728, 8233430727608, 32247603683108

Offset

1,1

Comments

Diagonal of A206267.

Links

R. H. Hardin and Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (first 69 terms from R. H. Hardin).

Formula

Recurrence (for n>3): (n+1)*(3*n-2)*a(n) = (15*n^2-n-4)*a(n-1) - 2*(2*n-1)*(3*n+1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) = 8+2*C(2*n+1,n), for n>1. - Vaclav Kotesovec, Oct 28 2012

Example

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

Mathematica

Flatten[{16, Table[8+2*Binomial[2*n+1, n], {n, 2, 20}]}] (* Vaclav Kotesovec, Oct 28 2012 *)

Crossrefs

Sequence in context: A357264 A349418 A184031 * A064803 A220762 A353597

Adjacent sequences: A206256 A206257 A206258 * A206260 A206261 A206262

Keyword

nonn

Author

R. H. Hardin, Feb 05 2012

Status

approved