A243384 Number of length n+3 0..3 arrays with no four elements in a row with pattern abba (with a!=b) and new values 0..3 introduced in 0..3 order.

14, 45, 158, 579, 2165, 8173, 30991, 117755, 447850, 1704019, 6484899, 24681529, 93941906, 357565151, 1360989974, 5180318659, 19717818240, 75051888869, 285669958665, 1087345593405, 4138764004397, 15753379857391, 59962100096460

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 16*a(n-2) + 18*a(n-3) - 15*a(n-4) + 9*a(n-5) - 3*a(n-6) + a(n-7).

Empirical g.f.: x*(14 - 53*x + 67*x^2 - 59*x^3 + 40*x^4 - 13*x^5 + 5*x^6) / ((1 - x)*(1 - 2*x + x^2 - x^3)*(1 - 4*x + x^2 - x^3)). - Colin Barker, Nov 02 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....1....1....0....1....1....1....0....1....1....1....0....1....1....1
..0....1....0....2....1....0....2....1....1....2....2....2....0....1....0....0
..1....1....1....3....1....1....0....2....2....1....1....3....0....1....0....0
..2....1....2....0....1....1....2....2....1....0....0....1....0....2....2....2
..1....0....3....3....0....2....1....2....1....2....1....3....0....2....2....3

Crossrefs

Column 3 of A243389.

Sequence in context: A232872 A232855 A232791 * A242579 A206208 A328245

Adjacent sequences: A243381 A243382 A243383 * A243385 A243386 A243387

Keyword

nonn

Author

R. H. Hardin, Jun 04 2014

Status

approved