A123011 a(n) = 2*a(n-1) + 5*a(n-2) for n > 1; a(0) = 1, a(1) = 5.

1, 5, 15, 55, 185, 645, 2215, 7655, 26385, 91045, 314015, 1083255, 3736585, 12889445, 44461815, 153370855, 529050785, 1824955845, 6295165615, 21715110455, 74906048985, 258387650245, 891305545415, 3074549342055

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,5).

Formula

a(n) = ((3+2*sqrt(6))*(1+sqrt(6))^n + (3-2*sqrt(6))*(1-sqrt(6))^n)/6. - Klaus Brockhaus, Aug 15 2009

From Klaus Brockhaus, Aug 15 2009: (Start)

G.f.: (1+3*x)/(1-2*x-5*x^2).

Binomial transform of A164532.

Inverse binomial transform of A164549. (End)

a(n) = (sqrt(5)*i)^(n-1)*(sqrt(5)*i*ChebyshevU(n, -i/sqrt(5)) + 3*ChebyshevU(n-1, -i/sqrt(5))) for n > 0 with a(0) = 1. - G. C. Greubel, Jul 13 2021

Mathematica

LinearRecurrence[{2, 5}, {1, 5}, 31] (* G. C. Greubel, Jul 13 2021 *)

Prog

(Magma) [ n le 2 select 4*n-3 else 2*Self(n-1)+5*Self(n-2): n in [1..24] ]; // Klaus Brockhaus, Aug 15 2009
(SageMath) [1]+[(sqrt(5)*i)^(n-1)*(sqrt(5)*i*chebyshev_U(n, -i/sqrt(5)) + 3*chebyshev_U(n-1, -i/sqrt(5))) for n in (1..30)] # G. C. Greubel, Jul 13 2021
(PARI) a(n)=([0, 1; 5, 2]^n*[1; 5])[1, 1] \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A002532, A164532, A164549.

Sequence in context: A243076 A002221 A007714 * A006358 A054108 A149585

Adjacent sequences: A123008 A123009 A123010 * A123012 A123013 A123014

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 23 2006

Extensions

Edited by N. J. A. Sloane, Aug 27 2009, using simpler definition suggested by Klaus Brockhaus, Aug 15 2009

Status

approved