A256818 Number of length n+3 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

16, 32, 64, 128, 245, 442, 753, 1220, 1894, 2836, 4118, 5824, 8051, 10910, 14527, 19044, 24620, 31432, 39676, 49568, 61345, 75266, 91613, 110692, 132834, 158396, 187762, 221344, 259583, 302950, 351947, 407108, 469000, 538224, 615416, 701248

Offset

1,1

Comments

Row 3 of A256816.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/12)*n^4 + (31/24)*n^3 - (31/12)*n^2 + (66/5)*n + 4.

Empirical g.f.: x*(16 - 64*x + 112*x^2 - 96*x^3 + 37*x^4 - 4*x^5) / (1 - x)^6. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A256816.

Sequence in context: A335161 A239751 A261782 * A048170 A340624 A067053

Adjacent sequences: A256815 A256816 A256817 * A256819 A256820 A256821

Keyword

nonn

Author

R. H. Hardin, Apr 10 2015

Status

approved