A251271 Number of (4+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.

337, 2058, 9109, 32636, 100843, 279718, 715685, 1722176, 3954037, 8757506, 18871133, 39828260, 82762159, 170015870, 346360653, 701430696, 1414589161, 2844655514, 5709353797, 11444200908, 22920272755, 45879723734, 91806810133

Offset

1,1

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 54*a(n-2) + 156*a(n-3) - 294*a(n-4) + 378*a(n-5) - 336*a(n-6) + 204*a(n-7) - 81*a(n-8) + 19*a(n-9) - 2*a(n-10).

Conjectures from Colin Barker, Nov 27 2018: (Start)

G.f.: x*(337 - 1649*x + 4669*x^2 - 9003*x^3 + 11763*x^4 - 10549*x^5 + 6447*x^6 - 2573*x^7 + 606*x^8 - 64*x^9) / ((1 - x)^9*(1 - 2*x)).

a(n) = (20160*(1369*2^n-1365) - 18907464*n - 6363848*n^2 - 1352064*n^3 - 190036*n^4 - 16401*n^5 - 637*n^6 + 9*n^7 + n^8) / 2520.

(End)

Example

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

Crossrefs

Row 4 of A251268.

Sequence in context: A142830 A160069 A201852 * A263865 A184202 A194478

Adjacent sequences: A251268 A251269 A251270 * A251272 A251273 A251274

Keyword

nonn

Author

R. H. Hardin, Dec 01 2014

Status

approved