A110273 a(n) = Pell(n)^3 + Pell(n+1)^3.

1, 9, 133, 1853, 26117, 367389, 5169809, 72744121, 1023588937, 14402985777, 202665398173, 2851718540021, 40126725007181, 564625868522949, 7944888884612393, 111793070252410993, 1573047872420021137

Offset

0,2

Links

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

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

Formula

G.f.: (1+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) = ( 3*(-1)^n*A001333(n) + (Pell(3*n) + Pell(3*(n+1)) )/8.

Mathematica

LinearRecurrence[{12, 30, -12, -1}, {1, 9, 133, 1853}, 30] (* Harvey P. Dale, Jan 24 2018 *)
Sum[Fibonacci[Range[0, 30] +j, 2]^3, {j, 0, 1}] (* G. C. Greubel, Sep 17 2021 *)

Prog

(Magma) I:=[1, 9, 133, 1853]; [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+1, 2, -1)^3 + lucas_number1(n, 2, -1)^3 for n in (0..30)] # G. C. Greubel, Sep 17 2021

Crossrefs

Cf. A000129, A110272.

Sequence in context: A366017 A097999 A089547 * A082760 A268654 A112426

Adjacent sequences: A110270 A110271 A110272 * A110274 A110275 A110276

Keyword

easy,nonn

Author

Paul Barry, Jul 18 2005

Status

approved