A206263 Number of (n+1) X 5 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.

50, 64, 135, 260, 471, 800, 1296, 2010, 3012, 4376, 6197, 8576, 11637, 15512, 20358, 26342, 33658, 42512, 53139, 65788, 80739, 98288, 118764, 142514, 169920, 201384, 237345, 278264, 324641, 377000, 435906, 501950, 575766, 658016, 749407, 850676

Offset

1,1

Comments

Column 4 of A206267.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) -a(n-7) for n>8.

Conjectures from Colin Barker, Jun 15 2018: (Start)

G.f.: x*(50 - 186*x + 265*x^2 - 89*x^3 - 184*x^4 + 240*x^5 - 114*x^6 + 20*x^7) / ((1 - x)^6*(1 + x)).

a(n) = (1680 + 1044*n + 580*n^2 + 155*n^3 + 20*n^4 + n^5) / 120 for n>1 and even.

a(n) = (1800 + 1044*n + 580*n^2 + 155*n^3 + 20*n^4 + n^5) / 120 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A206267.

Sequence in context: A179796 A215468 A109552 * A007692 A025285 A092541

Adjacent sequences: A206260 A206261 A206262 * A206264 A206265 A206266

Keyword

nonn

Author

R. H. Hardin, Feb 05 2012

Status

approved