A268256 Number of length-(n+1) 0..3 arrays with new repeated values introduced in sequential order starting with zero.

13, 43, 143, 479, 1616, 5492, 18804, 64869, 225483, 789747, 2787100, 9910252, 35501416, 128109313, 465606659, 1704022367, 6278399432, 23282368196, 86873186508, 326055377709, 1230562324251, 4668500002491, 17797745988388

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 60*a(n-2) + 105*a(n-3) - 11*a(n-4) - 94*a(n-5) - 24*a(n-6).

Empirical g.f.: x*(13 - 126*x + 364*x^2 - 165*x^3 - 403*x^4 - 96*x^5) / ((1 - 3*x)*(1 - 4*x)*(1 - 3*x - x^2)*(1 - 3*x - 2*x^2)). - Colin Barker, Jan 11 2019

Example

Some solutions for n=8:
..0....0....1....1....0....2....0....1....2....2....0....0....2....2....3....0
..1....2....2....3....1....3....0....0....0....3....1....3....1....1....0....0
..3....0....3....0....2....0....0....3....0....1....3....1....0....3....1....0
..2....2....1....1....3....0....3....0....0....0....2....0....0....2....0....1
..3....1....0....0....2....1....2....0....1....3....3....3....0....0....3....0
..2....2....1....0....1....2....1....3....3....1....0....2....1....0....2....0
..1....3....2....1....3....1....3....1....0....0....0....0....3....2....1....0
..2....0....1....1....1....0....2....0....3....0....3....0....1....3....0....1
..0....3....2....3....3....1....0....3....2....3....2....1....2....1....1....2

Crossrefs

Column 3 of A268261.

Sequence in context: A067260 A135241 A225774 * A243894 A303740 A243029

Adjacent sequences: A268253 A268254 A268255 * A268257 A268258 A268259

Keyword

nonn

Author

R. H. Hardin, Jan 29 2016

Status

approved