A256821 Number of length n+6 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

128, 256, 512, 1024, 1888, 3204, 5088, 7677, 11120, 15579, 21230, 28264, 36888, 47326, 59820, 74631, 92040, 112349, 135882, 162986, 194032, 229416, 269560, 314913, 365952, 423183, 487142, 558396, 637544, 725218, 822084, 928843, 1046232

Offset

1,1

Comments

Row 6 of A256816.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (111/8)*n^3 - (701/24)*n^2 + (11767/60)*n - 253 for n>4.

Empirical g.f.: x*(128 - 512*x + 896*x^2 - 768*x^3 + 224*x^4 + 68*x^5 - 24*x^6 - 7*x^7 - 14*x^8 + 10*x^9) / (1 - x)^6. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A256816.

Sequence in context: A110290 A045028 A255997 * A172421 A355919 A235059

Adjacent sequences: A256818 A256819 A256820 * A256822 A256823 A256824

Keyword

nonn

Author

R. H. Hardin, Apr 10 2015

Status

approved