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A243516 Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order. 1
3, 5, 10, 25, 77, 280, 1156, 5267, 25915, 135214, 736706, 4139833, 23767897, 138468212, 814675840, 4824766303, 28699128503, 171207852154, 1023332115838, 6124430348357, 36684624841813, 219860794899520, 1318179574171580 (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) = 17*a(n-1) - 111*a(n-2) + 355*a(n-3) - 584*a(n-4) + 468*a(n-5) - 144*a(n-6).

Conjectures from Colin Barker, Nov 02 2018: (Start)

G.f.: x*(3 - 46*x + 258*x^2 - 655*x^3 + 739*x^4 - 288*x^5) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)).

a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.

(End)

EXAMPLE

All solutions for n=3:

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

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

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

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

..3....1....2....0....0....4....3....1....0....1

CROSSREFS

Column 7 of A243519.

Sequence in context: A002039 A243514 A243515 * A243517 A243518 A025486

Adjacent sequences:  A243513 A243514 A243515 * A243517 A243518 A243519

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 05 2014

STATUS

approved

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Last modified August 1 17:43 EDT 2021. Contains 346402 sequences. (Running on oeis4.)