%I #16 Aug 31 2022 09:10:37

%S 1,1,1,5,9,17,41,85,177,385,817,1733,3705,7889,16793,35797,76257,

%T 162433,346081,737285,1570665,3346193,7128713,15186901,32354193,

%U 68927233,146842129,312831941,666455769,1419814097,3024765689,6443947093

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

%C Binomial transform is A099214. Binomial transform of A099212.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,3).

%F G.f.: (1-x^2)/(1-x-x^2-3*x^3). [corrected by _Michel Marcus_, Aug 31 2022]

%o (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

%o (PARI) Vec((1-x^2)/(1-x-x^2-3*x^3) + O(x^30)) \\ _Michel Marcus_, Aug 31 2022

%Y Cf. A099212, A099214.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Oct 06 2004