A155179 a(n) = 4*a(n-1)+a(n-2), n>2; a(0)=1, a(1)=3, a(2)=12.

1, 3, 12, 51, 216, 915, 3876, 16419, 69552, 294627, 1248060, 5286867, 22395528, 94868979, 401871444, 1702354755, 7211290464, 30547516611, 129401356908, 548152944243, 2322013133880, 9836205479763, 41666835052932, 176503545691491, 747681017818896, 3167227616967075

Offset: 0

Author

Philippe Deléham, Jan 21 2009

Keywords

• nonn
• easy

Comments

For n > 0, integers in 3/2 * the Fibonacci sequence. - Vladimir Joseph Stephan Orlovsky, Oct 25 2009

Links

• Stefano Spezia, Table of n, a(n) for n = 0..1500
• Index entries for linear recurrences with constant coefficients, signature (4,1).

Crossrefs

Cf. A155161.

Programs

Mathematica

f[n_]:=Fibonacci[n]; lst={};Do[a=f[n]*(3/2);If[IntegerQ[a],AppendTo[lst,a]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2009 *)

PARI

Vec((1-x-x^2)/((1-4*x-x^2)+O(x^99))) \\ Charles R Greathouse IV, Dec 09 2014

PARI

concat(1,select(n->denominator(n)==1,[fibonacci(n)*3/2|n<-[1..50]])) \\ Charles R Greathouse IV, Dec 09 2014

Formula

G.f.: (1-x-x^2)/(1-4*x-x^2).

a(n) = Sum_{k=0..n} A155161(n,k)*3^k. - Philippe Deléham, Feb 08 2012

E.g.f.: 1 + 3*exp(2*x)*sinh(sqrt(5)*x)/sqrt(5). - Stefano Spezia, Oct 06 2024

Extensions

Entries corrected by Paolo P. Lava, Jan 26 2009