A255627 Number of length n+5 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.

729, 2187, 6561, 17622, 40659, 83325, 156563, 275166, 458604, 731981, 1127139, 1683927, 2451654, 3490746, 4874628, 6691853, 9048501, 12070872, 15908498, 20737500, 26764317, 34229835, 43413945, 54640560, 68283122, 84770631

Offset

1,1

Comments

Row 5 of A255622.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (19/10080)*n^7 + (31/576)*n^6 + (122/45)*n^5 + (188527/5760)*n^4 + (32263/1440)*n^3 + (276001/672)*n^2 - (152493/280)*n + 387 for n>3.

Empirical g.f.: x*(729 - 4374*x + 13122*x^2 - 23931*x^3 + 26403*x^4 - 15630*x^5 + 2474*x^6 + 1593*x^7 + 693*x^8 - 1849*x^9 + 924*x^10 - 153*x^11) / (1 - x)^9. - Colin Barker, Jan 20 2018

Example

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

Crossrefs

Cf. A255622.

Sequence in context: A267697 A232925 A255112 * A139308 A295024 A167728

Adjacent sequences: A255624 A255625 A255626 * A255628 A255629 A255630

Keyword

nonn

Author

R. H. Hardin, Feb 28 2015

Status

approved