A142588 A trisection of A000129, the Pell numbers.

0, 5, 70, 985, 13860, 195025, 2744210, 38613965, 543339720, 7645370045, 107578520350, 1513744654945, 21300003689580, 299713796309065, 4217293152016490, 59341817924539925, 835002744095575440, 11749380235262596085, 165326326037771920630, 2326317944764069484905

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..850

Index entries for linear recurrences with constant coefficients, signature (14,1).

Formula

a(n) = A000129(3n).

From R. J. Mathar, Sep 22 2008: (Start)

G.f.: 5*x/(1-14*x-x^2).

a(n) = 5*A041085(n-1). (End)

a(n) = ( (7+5*sqrt(2))^n - (7-5*sqrt(2))^n) )/( 2*sqrt(2) ). - Colin Barker, Jan 25 2016

Mathematica

LinearRecurrence[{14, 1}, {0, 5}, 20] (* Harvey P. Dale, Jul 05 2019 *)
Fibonacci[3*Range[0, 30], 2] (* G. C. Greubel, Apr 13 2021 *)

Prog

(PARI) concat(0, Vec(5*x/(1-14*x-x^2) + O(x^20))) \\ Colin Barker, Jan 25 2016
(Magma) [n le 2 select 5*(n-1) else 14*Self(n-1) +Self(n-2): n in [1..31]]; // G. C. Greubel, Apr 13 2021
(Sage) [lucas_number1(3*n, 2, -1) for n in (0..30)] # G. C. Greubel, Apr 13 2021

Crossrefs

Cf. A000129, A041085.

Sequence in context: A034944 A064046 A256235 * A246154 A151471 A077691

Adjacent sequences: A142585 A142586 A142587 * A142589 A142590 A142591

Keyword

nonn,easy

Author

Paul Curtz, Sep 22 2008

Extensions

Changed offset and extended by R. J. Mathar, Sep 22 2008

Status

approved