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

Author

R. H. Hardin, Feb 14 2015

Keywords

• nonn

Comments

Column 4 of A255107.

Examples

			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
		

Links

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

Crossrefs

Cf. A255107.

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