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

Author

Paul Curtz, Sep 22 2008

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..850
• Index entries for linear recurrences with constant coefficients, signature (14,1).

Crossrefs

Cf. A000129, A041085.

Programs

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

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 *)

PARI

concat(0, Vec(5*x/(1-14*x-x^2) + O(x^20))) \\ Colin Barker, Jan 25 2016

Sage

[lucas_number1(3*n,2,-1) for n in (0..30)] # G. C. Greubel, Apr 13 2021

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

Extensions

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