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%I #23 Feb 26 2020 04:15:24
%S 1,1,6,21,81,306,1161,4401,16686,63261,239841,909306,3447441,13070241,
%T 49553046,187869861,712268721,2700415746,10238053401,38815407441,
%U 147160382526,557927369901,2115263257281,8019571881546,30404505416481
%N a(0)=a(1)=1; a(n) = 3*(a(n-1) + a(n-2)).
%H Joshua Zucker, Feb 23 2008, <a href="/A134927/b134927.txt">Table of n, a(n) for n = 0..50</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,3).
%F From _R. J. Mathar_, Jan 31 2008: (Start)
%F O.g.f.: (-1+2*x)/(-1 + 3*x + 3*x^2).
%F a(n) = A030195(n+1)-2*A030195(n). (End)
%F a(n) = A108306(n-1), n>0. - _R. J. Mathar_, Oct 04 2011
%F a(n) ~ 3.7912878474...^n, where the constant is A090458. - _Charles R Greathouse IV_, Oct 04 2011
%p 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
%t LinearRecurrence[{3, 3}, {1, 1}, 30]
%o (Sage)
%o from sage.combinat.sloane_functions import recur_gen2
%o it = recur_gen2(1,1,3,3)
%o [next(it) for i in range(25)] # _Zerinvary Lajos_, Jun 25 2008
%o (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
%K nonn,easy
%O 0,3
%A _Rolf Pleisch_, Jan 29 2008
%E More terms from _Joshua Zucker_, Feb 23 2008
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