A255995 Number of length n+4 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

32, 64, 100, 144, 196, 257, 328, 410, 504, 611, 732, 868, 1020, 1189, 1376, 1582, 1808, 2055, 2324, 2616, 2932, 3273, 3640, 4034, 4456, 4907, 5388, 5900, 6444, 7021, 7632, 8278, 8960, 9679, 10436, 11232, 12068, 12945, 13864, 14826, 15832, 16883, 17980

Offset

1,1

Comments

Row 4 of A255992.

Links

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

Formula

Empirical: a(n) = (1/6)*n^3 + 2*n^2 + (143/6)*n + 6 for n>2.

Empirical g.f.: x*(32 - 64*x + 36*x^2 - 4*x^4 + x^5) / (1 - x)^4. - Colin Barker, Jan 25 2018

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A376254 A122616 A174312 * A144908 A172419 A069492

Adjacent sequences: A255992 A255993 A255994 * A255996 A255997 A255998

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved