A206262 Number of (n+1) X 4 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.

34, 44, 78, 135, 218, 339, 503, 724, 1009, 1374, 1828, 2389, 3068, 3885, 4853, 5994, 7323, 8864, 10634, 12659, 14958, 17559, 20483, 23760, 27413, 31474, 35968, 40929, 46384, 52369, 58913, 66054, 73823, 82260, 91398, 101279, 111938, 123419, 135759

Offset

1,1

Comments

Column 3 of A206267.

Links

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

Formula

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

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

G.f.: x*(34 - 92*x + 72*x^2 + 43*x^3 - 102*x^4 + 58*x^5 - 11*x^6) / ((1 - x)^5*(1 + x)).

a(n) = (336 + 154*n + 71*n^2 + 14*n^3 + n^4) / 24 for n>1 and even.

a(n) = (312 + 154*n + 71*n^2 + 14*n^3 + n^4) / 24 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A206267.

Sequence in context: A076772 A359331 A248527 * A302457 A063470 A089715

Adjacent sequences: A206259 A206260 A206261 * A206263 A206264 A206265

Keyword

nonn

Author

R. H. Hardin, Feb 05 2012

Status

approved