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A072264 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=1. 7
1, 1, 8, 29, 127, 526, 2213, 9269, 38872, 162961, 683243, 2864534, 12009817, 50352121, 211105448, 885076949, 3710758087, 15557659006, 65226767453, 273468597389, 1146539629432, 4806961875241, 20153583772883, 84495560694854, 354254600948977, 1485241606321201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (3,5).

FORMULA

G.f.: (1-2*x)/(1-3*x-5*x^2). - Jaume Oliver Lafont, Mar 06 2009

a(n) = (1/2)*(((3/2)+(1/2)*sqrt(29))^n+((3/2)-(1/2)*sqrt(29))^n)+(1/58)*sqrt(29)*(((3/2)-(1/2)*sqrt(29))^n-((3/2)+(1/2)*sqrt(29))^n). - Paolo P. Lava, Mar 31 2009

G.f.: G(0)*(1-2*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

EXAMPLE

a(5)=3*a(4)+5*a(3): 127=3*29+5*8=87+40.

MATHEMATICA

LinearRecurrence[{3, 5}, {1, 1}, 30] (* Harvey P. Dale, Feb 17 2018 *)

PROG

(MAGMA) [n le 2 select 1 else 3*Self(n-1)+5*Self(n-2): n in [1..26]];  // Bruno Berselli, Oct 11 2011

CROSSREFS

Cf. A015523, A072263, A152187, A179606, A197189.

Sequence in context: A261478 A199207 A088131 * A110527 A189946 A239855

Adjacent sequences:  A072261 A072262 A072263 * A072265 A072266 A072267

KEYWORD

nonn,easy

AUTHOR

Miklos Kristof, Jul 08 2002

EXTENSIONS

Offset changed and more terms added by Bruno Berselli, Oct 11 2011

STATUS

approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)