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

1,1

Comments

Row 2 of A255660.

Links

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

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

Example

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

Crossrefs

Cf. A255660.

Sequence in context: A017066 A141478 A107262 * A045029 A231528 A333604

Adjacent sequences: A255659 A255660 A255661 * A255663 A255664 A255665

Keyword

nonn

Author

R. H. Hardin, Mar 01 2015

Status

approved