A000781 a(n) = 3*Catalan(n) - Catalan(n-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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A000108, A000782.

Programs

Mathematica

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

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