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A110272 a(n) = Pell(n)^3. 5
0, 1, 8, 125, 1728, 24389, 343000, 4826809, 67917312, 955671625, 13447314152, 189218084021, 2662500456000, 37464224551181, 527161643971768, 7417727240640625, 104375343011770368, 1468672529408250769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..850

Toufik Mansour, A formula for the generating functions of powers of Horadam's sequence, Australas. J. Combin. 30 (2004) 207-212.

Index entries for linear recurrences with constant coefficients, signature (12,30,-12,-1).

FORMULA

G.f.: x*(1-4*x-x^2) / ((1+2*x-x^2)*(1-14*x-x^2)).

a(n) = 12*a(n-1) + 30*a(n-2) - 12*a(n-3) - a(n-4).

a(n) = (Pell(3*n) - 3*(-1)^n*Pell(n))/8.

MATHEMATICA

Fibonacci[Range[0, 30], 2]^3 (* G. C. Greubel, Sep 17 2021 *)

PROG

(Magma) I:=[0, 1, 8, 125]; [n le 4 select I[n] else 12*Self(n-1) + 30*Self(n-2) -12*Self(n-3) - Self(n-4): n in [1..31]]; // G. C. Greubel, Sep 17 2021

(Sage) [lucas_number1(n, 2, -1)^3 for n in (0..30)] # G. C. Greubel, Sep 17 2021

CROSSREFS

Cf. A000129, A079291, A213688.

Sequence in context: A016791 A061103 A264143 * A215040 A033536 A355762

Adjacent sequences: A110269 A110270 A110271 * A110273 A110274 A110275

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jul 18 2005

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)