A099213 a(n) = a(n-1)+a(n-2)+3a(n-3), with a(0)=a(1)=a(2)=1.

1, 1, 1, 5, 9, 17, 41, 85, 177, 385, 817, 1733, 3705, 7889, 16793, 35797, 76257, 162433, 346081, 737285, 1570665, 3346193, 7128713, 15186901, 32354193, 68927233, 146842129, 312831941, 666455769, 1419814097, 3024765689, 6443947093

Offset: 0

Author

Paul Barry, Oct 06 2004

Keywords

• easy
• nonn

Comments

Binomial transform is A099214. Binomial transform of A099212.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,3).

Crossrefs

Cf. A099212, A099214.

Programs

PARI

Vec((1-x^2)/(1-x-x^2-3*x^3) + O(x^30)) \\ Michel Marcus, Aug 31 2022

Sage

from sage.combinat.sloane_functions import recur_gen3; it = recur_gen3(1,1,1,1,1,3); [next(it) for i in range(32)] # Zerinvary Lajos, Jun 25 2008

Formula

G.f.: (1-x^2)/(1-x-x^2-3*x^3). [corrected by Michel Marcus, Aug 31 2022]