A255110 Number of length n+3 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

81, 216, 441, 789, 1302, 2032, 3042, 4407, 6215, 8568, 11583, 15393, 20148, 26016, 33184, 41859, 52269, 64664, 79317, 96525, 116610, 139920, 166830, 197743, 233091, 273336, 318971, 370521, 428544, 493632, 566412, 647547, 737737, 837720, 948273

Offset

1,1

Comments

Row 3 of A255107.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/4)*n^4 + (59/24)*n^3 + (93/4)*n^2 + (1321/30)*n + 11.

Empirical g.f.: x*(81 - 270*x + 360*x^2 - 237*x^3 + 78*x^4 - 11*x^5) / (1 - x)^6. - Colin Barker, Jan 24 2018

Example

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

Crossrefs

Cf. A255107.

Sequence in context: A236728 A236877 A236721 * A062532 A075730 A184068

Adjacent sequences: A255107 A255108 A255109 * A255111 A255112 A255113

Keyword

nonn

Author

R. H. Hardin, Feb 14 2015

Status

approved