A258731 Number of length n+1 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

16, 60, 190, 512, 1212, 2592, 5115, 9460, 16588, 27820, 44928, 70240, 106760, 158304, 229653, 326724, 456760, 628540, 852610, 1141536, 1510180, 1976000, 2559375, 3283956, 4177044, 5269996, 6598660, 8203840, 10131792, 12434752, 15171497

Offset: 1

Author

R. H. Hardin, Jun 08 2015

Keywords

• nonn

Comments

Row 1 of A258730.

Examples

			Some solutions for n=4:
..3....1....0....1....0....0....2....1....3....0....0....1....1....1....3....3
..3....3....1....2....0....0....3....2....0....2....2....2....1....1....0....3
..2....3....0....2....0....0....1....0....0....0....2....3....2....1....1....1
..2....1....3....2....2....2....2....1....1....0....3....1....3....3....1....3
..2....1....3....2....1....2....3....1....1....1....3....2....3....0....2....3
		

Links

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

Crossrefs

Cf. A258730.

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/144)*n^6 + (73/720)*n^5 + (91/144)*n^4 + (179/90)*n^3 + (139/36)*n^2 + (568/105)*n + 4.

Empirical g.f.: x*(2 - x)*(8 - 30*x + 64*x^2 - 80*x^3 + 58*x^4 - 23*x^5 + 4*x^6) / (1 - x)^8. - Colin Barker, Jan 26 2018