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

Author

R. H. Hardin, Feb 14 2015

Keywords

• nonn

Comments

Row 7 of A255107.

Examples

			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
		

Links

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

Crossrefs

Cf. A255107.

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