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

0,4

Comments

Binomial transform is A099214. Binomial transform of A099212.

Links

Table of n, a(n) for n=0..31.

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

Formula

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

Prog

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

Crossrefs

Cf. A099212, A099214.

Sequence in context: A147401 A062536 A324718 * A146067 A336139 A295627

Adjacent sequences: A099210 A099211 A099212 * A099214 A099215 A099216

Keyword

easy,nonn

Author

Paul Barry, Oct 06 2004

Status

approved