A256820 Number of length n+5 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

64, 128, 256, 512, 956, 1656, 2693, 4158, 6153, 8792, 12202, 16524, 21914, 28544, 36603, 46298, 57855, 71520, 87560, 106264, 127944, 152936, 181601, 214326, 251525, 293640, 341142, 394532, 454342, 521136, 595511, 678098, 769563, 870608, 981972

Offset

1,1

Comments

Row 5 of A256816.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/6)*n^4 + (175/24)*n^3 - (103/6)*n^2 + (747/10)*n - 30 for n>3.

Empirical g.f.: x*(64 - 256*x + 448*x^2 - 384*x^3 + 124*x^4 + 16*x^5 - 7*x^6 - 8*x^7 + 4*x^8) / (1 - x)^6. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A256816.

Sequence in context: A172420 A069493 A076470 * A031464 A045076 A235058

Adjacent sequences: A256817 A256818 A256819 * A256821 A256822 A256823

Keyword

nonn

Author

R. H. Hardin, Apr 10 2015

Status

approved