A243027 Number of length n+3 0..2 arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..2 introduced in 0..2 order.

12, 32, 85, 226, 601, 1598, 4249, 11298, 30041, 79878, 212393, 564746, 1501641, 3992814, 10616761, 28229618, 75061625, 199586390, 530693641, 1411096922, 3752060265, 9976604734, 26527463577, 70535652418, 187551977881, 498694535334

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(12 + 8*x + 9*x^2) / (1 - 2*x - x^2 - 2*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
..0....0....1....1....1....0....1....1....1....1....0....1....1....0....1....1
..1....0....0....0....2....1....2....1....0....2....1....0....1....1....2....0
..2....1....1....1....0....0....2....2....0....1....2....2....1....2....0....1
..1....1....2....1....0....2....2....0....2....1....2....2....2....1....2....2
..0....1....0....1....0....0....0....0....1....1....2....2....2....1....0....1

Crossrefs

Column 2 of A243033.

Sequence in context: A332595 A188183 A183682 * A242543 A194644 A068381

Adjacent sequences: A243024 A243025 A243026 * A243028 A243029 A243030

Keyword

nonn

Author

R. H. Hardin, May 29 2014

Status

approved