A243028 Number of length n+3 0..3 arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..3 introduced in 0..3 order.

13, 42, 147, 536, 1987, 7414, 27736, 103868, 389129, 1458054, 5463618, 20473754, 76721788, 287502448, 1077370309, 4037278442, 15129079265, 56693899710, 212451684345, 796130077586, 2983375282018, 11179741027060, 41894363838109

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - a(n-2) + 2*a(n-3) - 6*a(n-4) - 2*a(n-5) - 3*a(n-6).

Empirical g.f.: x*(13 - 10*x - 8*x^2 - 36*x^3 - 16*x^4 - 14*x^5) / ((1 - x - x^3)*(1 - 3*x - 2*x^2 - 3*x^3)). - Colin Barker, Nov 01 2018

Example

Some solutions for n=3:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....0....1....1....0....1....0....1....1....1....1....0....1....0
..2....0....1....1....0....2....0....1....0....2....0....0....0....0....0....1
..2....2....0....2....0....3....1....1....1....0....1....2....2....1....1....2
..3....3....0....3....2....2....2....0....0....1....0....0....3....2....1....1
..0....0....0....3....0....2....3....1....2....2....2....0....2....0....1....1

Crossrefs

Column 3 of A243033.

Sequence in context: A139277 A162265 A233298 * A242544 A301539 A240517

Adjacent sequences: A243025 A243026 A243027 * A243029 A243030 A243031

Keyword

nonn

Author

R. H. Hardin, May 29 2014

Status

approved