A255114 Number of length n+7 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

6561, 14849, 19338, 23463, 29147, 38010, 49611, 63075, 78552, 96210, 116236, 138837, 164241, 192698, 224481, 259887, 299238, 342882, 391194, 444577, 503463, 568314, 639623, 717915, 803748, 897714, 1000440, 1112589, 1234861, 1367994

Offset

1,1

Comments

Row 7 of A255107.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (5/12)*n^4 + (187/24)*n^3 + (7393/12)*n^2 + (20667/10)*n + 1143 for n>5.

Empirical g.f.: x*(6561 - 24517*x + 28659*x^2 - 1050*x^3 - 20126*x^4 + 11682*x^5 - 2967*x^6 + 3385*x^7 - 168*x^8 - 2466*x^9 + 1008*x^10) / (1 - x)^6. - Colin Barker, Jan 24 2018

Example

Some solutions for n=4:
..0....0....1....1....1....1....0....0....0....2....1....2....2....2....0....2
..1....0....0....1....1....1....1....1....1....0....0....0....0....2....1....0
..1....2....0....1....0....1....1....2....1....0....0....2....0....0....0....0
..1....2....2....1....1....1....1....0....1....0....0....2....0....0....0....1
..2....0....2....0....1....0....0....2....2....1....1....2....0....1....2....1
..1....0....1....2....1....1....0....2....0....2....1....2....1....2....2....0
..1....0....1....2....2....1....1....2....0....0....2....0....2....2....2....0
..1....0....2....2....2....1....1....0....1....0....0....0....0....2....2....0
..1....2....2....0....0....0....2....0....1....1....2....1....0....2....0....1
..0....0....2....1....2....2....0....0....1....2....2....1....0....1....0....2
..2....1....2....2....2....2....1....0....2....0....2....0....2....1....0....2

Crossrefs

Cf. A255107.

Sequence in context: A043488 A046321 A043456 * A255629 A017080 A017164

Adjacent sequences: A255111 A255112 A255113 * A255115 A255116 A255117

Keyword

nonn

Author

R. H. Hardin, Feb 14 2015

Status

approved