A242544 Number of length n+3 0..3 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..3 introduced in 0..3 order

13, 42, 150, 554, 2072, 7808, 29536, 111878, 423969, 1607058, 6092367, 23097242, 87566957, 331989206, 1258663594, 4771951574, 18091832688, 68591328768, 260049450816, 985922294306, 3737915147525, 14171512153838, 53728281674119

Offset

1,1

Comments

Column 3 of A242549

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -2*a(n-4) -12*a(n-5) -9*a(n-6) -18*a(n-7) -9*a(n-8).

Empirical: G.f.: -x*(-13+10*x-21*x^2+50*x^3+88*x^4+78*x^5+99*x^6+42*x^7) / ( (x^2+x-1)*(3*x^2+3*x-1)*(3*x^2+1)*(x^2+1) ). - R. J. Mathar, May 18 2014

Example

Some solutions for n=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....1....0....1....1....1....1....1....1....1....1....1....1
..2....2....1....1....1....1....1....1....1....0....1....2....2....2....2....2
..1....1....2....0....2....0....2....2....2....0....2....3....1....0....1....3
..2....1....3....2....0....2....0....3....3....2....1....0....2....0....0....1
..2....1....0....0....1....3....0....3....3....1....3....2....0....3....1....0
..1....2....3....0....2....1....3....0....3....2....3....2....3....1....1....0

Crossrefs

Sequence in context: A162265 A233298 A243028 * A301539 A240517 A074022

Adjacent sequences: A242541 A242542 A242543 * A242545 A242546 A242547

Keyword

nonn

Author

R. H. Hardin, May 17 2014

Status

approved