A029848 a(n) = 1 + C(2*n,n) + C(3*n,n).

3, 6, 22, 105, 566, 3256, 19489, 119713, 748342, 4735446, 30229772, 194242153, 1254381857, 8132826045, 52900345681, 345022543105, 2255449994038, 14773402692946, 96935423713906, 637019314585501, 4191982352334316, 27619973660237476, 182185272080724121, 1202945209263916561

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000984, A096131.

Programs

GAP

List([0..20],n->1+Binomial(2*n,n)+Binomial(3*n,n)); # Muniru A Asiru, Aug 12 2018

Maple

a:=n->1+binomial(2*n,n)+binomial(3*n,n): seq(a(n),n=0..20); # Muniru A Asiru, Aug 12 2018

Mathematica

Table[1+Binomial[2n,n]+Binomial[3n,n],{n,0,30}] (* Harvey P. Dale, Jan 09 2019 *)

PARI

a(n) = 1 + binomial(2*n, n) + binomial(3*n, n); \\ Michel Marcus, Aug 12 2018

Formula

G.f.: 1/(1-x)+1/sqrt(1-4*x)+cos(arcsin((3^(3/2)*sqrt(x))/2)/3)/sqrt(1-(27*x)/4). - Vladimir Kruchinin, Aug 07 2025