A072264 a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=1.

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

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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

a(n) = 5^((n-1)/2)*( sqrt(5)*Fibonacci(n+1, 3/sqrt(5)) - 2*Fibonacci(n, 3/sqrt(5)) ). - G. C. Greubel, Jan 14 2020

Example

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

Maple

seq(coeff(series((1-2*x)/(1-3*x-5*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 14 2020

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
(PARI) my(x='x+O('x^30)); Vec((1-2*x)/(1-3*x-5*x^2)) \\ G. C. Greubel, Jan 14 2020
(Sage)
def A072264_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-2*x)/(1-3*x-5*x^2) ).list()
A072264_list(30) # G. C. Greubel, Jan 14 2020
(GAP) a:=[1, 1];; for n in [3..30] do a[n]:=3*a[n-1]+5*a[n-2]; od; a; # G. C. Greubel, Jan 14 2020

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