A255618 Number of length n+4 0..2 arrays with at most two downsteps in every 4 consecutive neighbor pairs.

237, 694, 2040, 5997, 17622, 51768, 152106, 446932, 1313199, 3858468, 11337057, 33310953, 97875387, 287580727, 844979241, 2482746381, 7294888809, 21434086890, 62978352609, 185045107303, 543705739710, 1597534436091, 4693929248088

Offset

1,1

Comments

Column 4 of A255622.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -a(n-3) +3*a(n-4) -3*a(n-5) -8*a(n-6) +9*a(n-7) -3*a(n-8) +a(n-9).

Empirical g.f.: x*(237 - 17*x - 42*x^2 + 114*x^3 - 386*x^4 - 429*x^5 + 657*x^6 - 216*x^7 + 81*x^8) / ((1 - x)*(1 - 2*x - 2*x^2 - x^3 - 4*x^4 - x^5 + 7*x^6 - 2*x^7 + x^8)). - Colin Barker, Jan 24 2018

Example

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

Crossrefs

Cf. A255622.

Sequence in context: A036270 A217030 A048454 * A237592 A256805 A192283

Adjacent sequences: A255615 A255616 A255617 * A255619 A255620 A255621

Keyword

nonn

Author

R. H. Hardin, Feb 28 2015

Status

approved