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A000781 a(n) = 3*Catalan(n)-Catalan(n-1)-1. 1
1, 4, 12, 36, 111, 353, 1154, 3860, 13155, 45525, 159561, 565249, 2020687, 7280419, 26410094, 96378164, 353576699, 1303271309, 4824150869, 17925098069, 66834680639, 249981423899, 937696277309, 3526652828321, 13295935057031, 50240112815003 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

John Cerkan, Table of n, a(n) for n = 1..1657

J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

FORMULA

G.f.: 1/2*(((Sqrt[1-4*x]-7)*x-3 Sqrt[1-4*x]+3)/x^2+2/(x-1)). - Harvey P. Dale, Apr 28 2013

Conjecture: 3*(n+1)*a(n) +(-19*n+7)*a(n-1) +(33*n-53)*a(n-2) +(-21*n+61)*a(n-3) +2*(2*n-9)*a(n-4)=0. - R. J. Mathar, Aug 20 2013

MATHEMATICA

3#[[2]]-#[[1]]-1&/@Partition[CatalanNumber[Range[0, 30]], 2, 1] (* Harvey P. Dale, Apr 28 2013 *)

CROSSREFS

Cf. A000108, A000782.

Sequence in context: A177881 A290899 A290905 * A192205 A055395 A113990

Adjacent sequences:  A000778 A000779 A000780 * A000782 A000783 A000784

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 6 10:50 EDT 2020. Contains 334843 sequences. (Running on oeis4.)