A242318 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A242318

Number of length n+3+2 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+3 elements, and new values 0..3 introduced in order.

65, 185, 503, 1316, 3398, 8801, 23069, 60197, 156887, 408962, 1066514, 2781611, 7253453, 18914369, 49323167, 128621684, 335409314, 874649537, 2280834353, 5947765493, 15510073823, 40445831522, 105471145814, 275038567523

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

FORMULA

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

Empirical g.f.: x*(65 + 120*x + 188*x^2 + 248*x^3 + 196*x^4 - 53*x^5 - 36*x^6 - 16*x^7 - 49*x^8 - 35*x^9) / (1 - x - 2*x^2 - 3*x^3 - 5*x^4 - 6*x^5 + x^6 + x^7 + x^9 + x^10). - Colin Barker, Nov 01 2018

EXAMPLE

Some solutions for n=5:

..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

..0....0....1....1....0....1....0....1....1....0....1....1....1....1....1....1

..0....1....0....2....1....1....1....2....1....1....2....2....2....1....2....2

..1....2....1....0....2....2....2....3....2....2....3....0....0....2....3....3

..2....3....2....3....0....3....3....1....3....3....2....3....1....1....0....1

..3....0....3....3....3....0....2....2....0....1....0....2....3....3....1....1

..1....1....0....1....2....1....0....0....1....0....3....2....2....0....3....0

..3....1....2....2....1....2....3....2....0....2....1....1....0....1....1....2

..0....2....1....0....3....1....1....3....2....3....0....2....2....2....2....0

..3....0....1....0....2....3....1....0....2....0....0....0....3....3....3....3

CROSSREFS

Column 3 of A242322.

Sequence in context: A255244 A261989 A051968 * A200867 A175795 A056777

Adjacent sequences: A242315 A242316 A242317 * A242319 A242320 A242321

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 10 2014

STATUS

approved