A256819 Number of length n+4 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

32, 64, 128, 256, 484, 856, 1424, 2249, 3402, 4965, 7032, 9710, 13120, 17398, 22696, 29183, 37046, 46491, 57744, 71052, 86684, 104932, 126112, 150565, 178658, 210785, 247368, 288858, 335736, 388514, 447736, 513979, 587854, 670007, 761120, 861912

Offset

1,1

Comments

Row 4 of A256816.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/8)*n^4 + (27/8)*n^3 - (65/8)*n^2 + (1897/60)*n + 3 for n>2.

Empirical g.f.: x*(32 - 128*x + 224*x^2 - 192*x^3 + 68*x^4 - 4*x^6 + x^7) / (1 - x)^6. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A256816.

Sequence in context: A172419 A069492 A076469 * A358250 A235057 A339358

Adjacent sequences: A256816 A256817 A256818 * A256820 A256821 A256822

Keyword

nonn

Author

R. H. Hardin, Apr 10 2015

Status

approved