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A142588 A trisection of A000129, the Pell numbers. 3
0, 5, 70, 985, 13860, 195025, 2744210, 38613965, 543339720, 7645370045, 107578520350, 1513744654945, 21300003689580, 299713796309065, 4217293152016490, 59341817924539925, 835002744095575440, 11749380235262596085, 165326326037771920630, 2326317944764069484905 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A034944 A064046 A256235 * A246154 A151471 A077691
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 22 2008
EXTENSIONS
Changed offset and extended by R. J. Mathar, Sep 22 2008
STATUS
approved

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Last modified June 20 22:01 EDT 2024. Contains 373532 sequences. (Running on oeis4.)