A134927 a(0)=a(1)=1; a(n) = 3*(a(n-1) + a(n-2)).

1, 1, 6, 21, 81, 306, 1161, 4401, 16686, 63261, 239841, 909306, 3447441, 13070241, 49553046, 187869861, 712268721, 2700415746, 10238053401, 38815407441, 147160382526, 557927369901, 2115263257281, 8019571881546, 30404505416481

Offset

0,3

Links

Joshua Zucker, Feb 23 2008, Table of n, a(n) for n = 0..50

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

Formula

From R. J. Mathar, Jan 31 2008: (Start)

O.g.f.: (-1+2*x)/(-1 + 3*x + 3*x^2).

a(n) = A030195(n+1)-2*A030195(n). (End)

a(n) = A108306(n-1), n>0. - R. J. Mathar, Oct 04 2011

a(n) ~ 3.7912878474...^n, where the constant is A090458. - Charles R Greathouse IV, Oct 04 2011

Maple

a[0]:=1:a[1]:=1:for n from 2 to 50 do a[n]:=3*a[n-1]+3*a[n-2] od: seq(a[n], n=0..33); # Zerinvary Lajos, Dec 14 2008

Mathematica

LinearRecurrence[{3, 3}, {1, 1}, 30]

Prog

(Sage)
from sage.combinat.sloane_functions import recur_gen2
it = recur_gen2(1, 1, 3, 3)
[next(it) for i in range(25)] # Zerinvary Lajos, Jun 25 2008
(PARI) a=[1, 1]; for(i=2, 10, a=concat(a, 3*a[#a]+3*a[#a-1])); a \\ Charles R Greathouse IV, Oct 04 2011

Crossrefs

Essentially the same as A108306.

Sequence in context: A026628 A053768 A255719 * A108306 A199115 A320649

Adjacent sequences: A134924 A134925 A134926 * A134928 A134929 A134930

Keyword

nonn,easy

Author

Rolf Pleisch, Jan 29 2008

Extensions

More terms from Joshua Zucker, Feb 23 2008

Status

approved