A197189 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=2.
1, 2, 11, 43, 184, 767, 3221, 13498, 56599, 237287, 994856, 4171003, 17487289, 73316882, 307387091, 1288745683, 5403172504, 22653245927, 94975600301, 398193030538, 1669457093119, 6999336432047, 29345294761736, 123032566445443, 515824173145009, 2162635351662242
Offset: 0
Links
- Bruno Berselli, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,5).
Programs
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Magma
[n le 2 select n else 3*Self(n-1)+5*Self(n-2): n in [1..26]];
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Mathematica
a = {1, 2}; Do[AppendTo[a, 3 a[[-1]] + 5 a[[-2]]], {24}]; a (* Bruno Berselli, Dec 26 2012 *) -
PARI
v=vector(26); v[1]=1; v[2]=2; for(i=3, #v, v[i]=3*v[i-1]+5*v[i-2]); v
Formula
G.f.: (1-x)/(1-3*x-5*x^2).
a(n) = ((29+sqrt(29))*(3+sqrt(29))^n+(29-sqrt(29))*(3-sqrt(29))^n)/(58*2^n).
G.f.: G(0)*(1-x)/(2-3*x), where G(k)= 1 + 1/(1 - x*(29*k-9)/(x*(29*k+20) - 6/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 17 2013