A114619 a(n) = 2*A079291(n) (twice squares of Pell numbers).

0, 2, 8, 50, 288, 1682, 9800, 57122, 332928, 1940450, 11309768, 65918162, 384199200, 2239277042, 13051463048, 76069501250, 443365544448, 2584123765442, 15061377048200, 87784138523762, 511643454094368

Offset: 0

Author

Creighton Dement, Feb 17 2006

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,5,-1).

Crossrefs

Cf. A000129, A001109, A001333, A001542, A079291.

Cf. also A090390, A108475, A114619, A116484.

Programs

Magma

[n le 3 select 2*(n-1)^2 else 5*Self(n-1) +5*Self(n-2) -Self(n-3): n in [1..31]]; // G. C. Greubel, Aug 18 2022

Mathematica

2*Fibonacci[Range[0, 30], 2]^2 (* G. C. Greubel, Aug 18 2022 *)

SageMath

[2*lucas_number1(n,2,-1)^2 for n in (0..30)] # G. C. Greubel, Aug 18 2022

Formula

a(n) = 2*A000129(n)^2.

G.f.: 2*x*(1-x)/((1+x)*(1-6*x+x^2)).

a(n) = A001333(n)^2 - (-1)^n. - Antonio Pane (apane1(AT)spc.edu), Dec 15 2007

Extensions

Entry revised by N. J. A. Sloane, Mar 15 2024