A255662 Number of length n+2 0..3 arrays with at most two downsteps in every n consecutive neighbor pairs.

64, 256, 1016, 3692, 11752, 33042, 83752, 195020, 423460, 867347, 1690744, 3158528, 5686080, 9908365, 16774260, 27673310, 44603624, 70391386, 108974472, 165764956, 248107880, 365856580, 532088128, 763986096, 1083921900, 1520770469

Offset: 1

Author

R. H. Hardin, Mar 01 2015

Keywords

• nonn

Comments

Row 2 of A255660.

Examples

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

Links

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

Crossrefs

Cf. A255660.

Formula

Empirical: a(n) = (1/39916800)*n^11 + (1/453600)*n^10 + (1/11520)*n^9 + (11/6048)*n^8 + (28751/1209600)*n^7 + (4303/21600)*n^6 + (789461/725760)*n^5 + (40955/18144)*n^4 + (164359/43200)*n^3 + (110513/6300)*n^2 + (44789/1540)*n + 10.

Empirical g.f.: x*(64 - 512*x + 2168*x^2 - 5684*x^3 + 9864*x^4 - 11798*x^5 + 9944*x^6 - 5948*x^7 + 2500*x^8 - 711*x^9 + 124*x^10 - 10*x^11) / (1 - x)^12. - Colin Barker, Jan 21 2018