A206264 Number of (n+1) X 6 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.

72, 93, 218, 471, 932, 1725, 3011, 5014, 8016, 12385, 18572, 27141, 38768, 54273, 74621, 100956, 134604, 177109, 230238, 296019, 376748, 475029, 593783, 736290, 906200, 1107577, 1344912, 1623169, 1947800, 2324793, 2760689, 3262632, 3838388

Offset

1,1

Comments

Column 5 of A206267.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>9.

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

G.f.: x*(72 - 339*x + 668*x^2 - 543*x^3 - 144*x^4 + 683*x^5 - 591*x^6 + 232*x^7 - 36*x^8) / ((1 - x)^7*(1 + x)).

a(n) = (11520 + 8028*n + 5104*n^2 + 1665*n^3 + 295*n^4 + 27*n^5 + n^6) / 720 for n>1 and even.

a(n) = (10800 + 8028*n + 5104*n^2 + 1665*n^3 + 295*n^4 + 27*n^5 + n^6) / 720 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A206267.

Sequence in context: A043967 A248970 A066943 * A063922 A063923 A030025

Adjacent sequences: A206261 A206262 A206263 * A206265 A206266 A206267

Keyword

nonn

Author

R. H. Hardin, Feb 05 2012

Status

approved