A243638 Number of length n+2 0..7 arrays with no three unequal elements in a row and new values 0..7 introduced in 0..7 order.

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133556, 386062, 1132106, 3365610, 10137369, 30919271, 95444507, 298042003, 941032182, 3002839544, 9679707876, 31506186516, 103497873819, 342976360273, 1146003129573

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 56*a(n-2) + 44*a(n-3) + 305*a(n-4) - 633*a(n-5) - 476*a(n-6) + 1772*a(n-7) + 308*a(n-8) - 2060*a(n-9) - 368*a(n-10) + 864*a(n-11) + 288*a(n-12).

Empirical g.f.: x*(4 - 43*x + 128*x^2 + 106*x^3 - 976*x^4 + 392*x^5 + 2696*x^6 - 1239*x^7 - 3714*x^8 + 363*x^9 + 2016*x^10 + 576*x^11) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 4*x^2)*(1 - 2*x - 6*x^2)). - Colin Barker, Nov 02 2018

Example

Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....0....0....1....1....1....1....0....1....0....1....0
..1....1....0....1....1....1....1....1....1....1....1....1....1....1....1....1
..0....0....1....1....0....1....1....2....1....0....0....0....2....0....2....0
..1....1....0....1....0....2....1....2....2....0....0....0....2....0....2....1
..0....1....1....1....1....1....0....0....2....1....2....1....2....0....0....0
..0....1....1....2....0....1....1....0....3....0....0....1....2....0....2....0
..0....0....1....1....1....1....0....3....3....0....0....2....2....0....0....1

Crossrefs

Column 7 of A243641.

Sequence in context: A243635 A243636 A243637 * A243639 A243640 A243634

Adjacent sequences: A243635 A243636 A243637 * A243639 A243640 A243641

Keyword

nonn

Author

R. H. Hardin, Jun 08 2014

Status

approved