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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.
1
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 05 2012
STATUS
approved