A255997 Number of length n+6 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

128, 256, 354, 451, 568, 705, 854, 1016, 1192, 1383, 1590, 1814, 2056, 2317, 2598, 2900, 3224, 3571, 3942, 4338, 4760, 5209, 5686, 6192, 6728, 7295, 7894, 8526, 9192, 9893, 10630, 11404, 12216, 13067, 13958, 14890, 15864, 16881, 17942, 19048, 20200

Offset

1,1

Comments

Row 6 of A255992.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + 3*n^2 + (533/6)*n + 28 for n>4.

Empirical g.f.: x*(128 - 256*x + 98*x^2 + 59*x^3 - 8*x^4 - 21*x^5 - 8*x^6 + 9*x^7) / (1 - x)^4. - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A110290 A045028 A378374 * A256821 A172421 A355919

Adjacent sequences: A255994 A255995 A255996 * A255998 A255999 A256000

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved