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A155179 a(n)=4*a(n-1)+a(n-2), n>2; a(0)=1, a(1)=3, a(2)=12. 2
1, 3, 12, 51, 216, 915, 3876, 16419, 69552, 294627, 1248060, 5286867, 22395528, 94868979, 401871444, 1702354755, 7211290464, 30547516611, 129401356908, 548152944243, 2322013133880, 9836205479763, 41666835052932 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..22.

FORMULA

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

a(n) = (3/2)*((2-sqrt(5))^(n-1)+(2+sqrt(5))^(n-1))+(3/5)*sqrt(5)*((2+sqrt(5))^(n-1)-(2-sqrt(5))^(n-1))+(C(2*n,n) mod 2). - Paolo P. Lava, Jan 26 2009

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

MATHEMATICA

Clear[f, lst, n, a] 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 *)

PROG

(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

CROSSREFS

Sequence in context: A043291 A135343 A083314 * A228770 A104268 A081704

Adjacent sequences:  A155176 A155177 A155178 * A155180 A155181 A155182

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Jan 21 2009

EXTENSIONS

Entries corrected by Paolo P. Lava, Jan 26 2009

STATUS

approved

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Last modified May 15 01:50 EDT 2021. Contains 343909 sequences. (Running on oeis4.)