

A197189


a(n) = 3*a(n1) + 5*a(n2), with a(0)=1, a(1)=2.


9



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
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OFFSET

0,2


LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,5).


FORMULA

G.f.: (1x)/(13*x5*x^2).
a(n) = ((29+sqrt(29))*(3+sqrt(29))^n+(29sqrt(29))*(3sqrt(29))^n)/(58*2^n).
a(n) = A015523(n+1)A015523(n).
G.f.: G(0)*(1x)/(23*x), where G(k)= 1 + 1/(1  x*(29*k9)/(x*(29*k+20)  6/G(k+1))); (continued fraction).  Sergei N. Gladkovskii, Jun 17 2013


MATHEMATICA

a = {1, 2}; Do[AppendTo[a, 3 a[[1]] + 5 a[[2]]], {24}]; a (* Bruno Berselli, Dec 26 2012 *)


PROG

(PARI) v=vector(26); v[1]=1; v[2]=2; for(i=3, #v, v[i]=3*v[i1]+5*v[i2]); v
(MAGMA) [n le 2 select n else 3*Self(n1)+5*Self(n2): n in [1..26]];


CROSSREFS

Cf. for type of recurrence: A015523, A072263, A072264, A152187, A179606 and also A180140.
Sequence in context: A027247 A141190 A048500 * A050620 A027253 A241712
Adjacent sequences: A197186 A197187 A197188 * A197190 A197191 A197192


KEYWORD

nonn,easy


AUTHOR

Bruno Berselli, Oct 11 2011


STATUS

approved



