A255103 Number of length n+4 0..2 arrays with at most one downstep in every 4 consecutive neighbor pairs.

147, 331, 789, 1905, 4429, 10125, 23463, 55246, 129480, 300432, 696375, 1623876, 3795126, 8845445, 20569653, 47880261, 111630444, 260248590, 606129714, 1411326056, 3287784315, 7661560197, 17850285244, 41578206276, 96850762992

Offset

1,1

Comments

Column 4 of A255107.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +12*a(n-4) -18*a(n-5) +7*a(n-6) -3*a(n-8) +a(n-9).

Empirical g.f.: x*(147 - 110*x + 237*x^2 + 384*x^3 - 1014*x^4 + 438*x^5 - 69*x^6 - 172*x^7 + 66*x^8) / (1 - 3*x + 3*x^2 - x^3 - 12*x^4 + 18*x^5 - 7*x^6 + 3*x^8 - x^9). - Colin Barker, Jan 24 2018

Example

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

Crossrefs

Cf. A255107.

Sequence in context: A259288 A325608 A375155 * A184542 A350638 A162701

Adjacent sequences: A255100 A255101 A255102 * A255104 A255105 A255106

Keyword

nonn

Author

R. H. Hardin, Feb 14 2015

Status

approved