A255109 Number of length n+2 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

27, 75, 168, 331, 597, 1008, 1616, 2484, 3687, 5313, 7464, 10257, 13825, 18318, 23904, 30770, 39123, 49191, 61224, 75495, 92301, 111964, 134832, 161280, 191711, 226557, 266280, 311373, 362361, 419802, 484288, 556446, 636939, 726467, 825768, 935619

Offset: 1

Author

R. H. Hardin, Feb 14 2015

Keywords

• nonn

Comments

Row 2 of A255107.

Examples

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

Links

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

Crossrefs

Cf. A255107.

Formula

Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (37/24)*n^3 + (175/24)*n^2 + (239/20)*n + 6.

Empirical g.f.: x*(3 - 3*x + x^2)*(9 - 20*x + 18*x^2 - 6*x^3) / (1 - x)^6. - Colin Barker, Jan 24 2018