A106569 a(n) = 5*a(n-1) + 3*a(n-2), where a(0) = 0, a(1) = 3.

0, 3, 15, 84, 465, 2577, 14280, 79131, 438495, 2429868, 13464825, 74613729, 413463120, 2291156787, 12696173295, 70354336836, 389860204065, 2160364030833, 11971400766360, 66338095924299, 367604681920575

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 (5,3).

Formula

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

a(n) = 3*A015536(n).

G.f.: 3*x/(1 - 5*x - 3*x^2). - G. C. Greubel, Sep 07 2021

Maple

a[0]:=0: a[1]:=3: for n from 2 to 23 do a[n]:= 5*a[n-1]+3*a[n-2] od: seq(a[n], n=0..23);

Mathematica

LinearRecurrence[{5, 3}, {0, 3}, 40] (* G. C. Greubel, Sep 07 2021 *)

Prog

(Magma) [n le 2 select 3*(n-1) else 5*Self(n-1) + 3*Self(n-2): n in [1..41]]; // G. C. Greubel, Sep 07 2021
(Sage) [3*lucas_number1(n, 5, -3) for n in (0..40)] # G. C. Greubel, Sep 07 2021

Crossrefs

Cf. A015536.

Sequence in context: A195885 A115910 A355094 * A260769 A026032 A005809

Adjacent sequences: A106566 A106567 A106568 * A106570 A106571 A106572

Keyword

nonn,easy,less

Author

Roger L. Bagula, May 30 2005

Extensions

Edited by N. J. A. Sloane, Apr 30 2006

New (corrected) name by G. C. Greubel, Sep 07 2021

Status

approved