A206261 Number of (n+1) X 3 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.

24, 28, 44, 64, 93, 128, 174, 228, 295, 372, 464, 568, 689, 824, 978, 1148, 1339, 1548, 1780, 2032, 2309, 2608, 2934, 3284, 3663, 4068, 4504, 4968, 5465, 5992, 6554, 7148, 7779, 8444, 9148, 9888, 10669, 11488, 12350, 13252, 14199, 15188, 16224, 17304

Offset

1,1

Comments

Column 2 of A206267.

Links

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

Formula

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

Conjectures from Colin Barker, Jun 14 2018: (Start)

G.f.: x*(24 - 44*x + 8*x^2 + 36*x^3 - 27*x^4 + 5*x^5) / ((1 - x)^4*(1 + x)).

a(n) = (72 + 26*n + 9*n^2 + n^3) / 6 for n>1 and even.

a(n) = (78 + 26*n + 9*n^2 + n^3) / 6 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A206267.

Sequence in context: A268540 A030500 A107406 * A217441 A045668 A045659

Adjacent sequences: A206258 A206259 A206260 * A206262 A206263 A206264

Keyword

nonn

Author

R. H. Hardin, Feb 05 2012

Status

approved