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
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).
Crossrefs
Essentially the same as A108306.
Programs
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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
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Mathematica
LinearRecurrence[{3, 3}, {1, 1}, 30] -
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
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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
Formula
From R. J. Mathar, Jan 31 2008: (Start)
O.g.f.: (-1+2*x)/(-1 + 3*x + 3*x^2).
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
Extensions
More terms from Joshua Zucker, Feb 23 2008