A133417 a(n) = sqrt(2*(P(n)^4 + 16*P(n+1)^4 + P(n+2)^4)), where P() = Pell numbers A000129.

2, 8, 42, 248, 1442, 8408, 49002, 285608, 1664642, 9702248, 56548842, 329590808, 1920996002, 11196385208, 65257315242, 380347506248, 2216827722242, 12920618827208, 75306885241002, 438920692618808, 2558217270471842, 14910382930212248, 86904080310801642, 506514098934597608

Offset

-1,1

Links

Colin Barker, Table of n, a(n) for n = -1..1000

J. L. Diaz-Barrero, Problem B-1029, Fib. Quart., 45 (2007), 86.

Index entries for linear recurrences with constant coefficients, signature (5,5,-1).

Formula

From Colin Barker, May 11 2012: (Start)

a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3).

G.f.: 2*x^-1*(1-x-4*x^2)/((1+x)*(1-6*x+x^2)). (End)

a(n) = (2*(-1)^n+5*(3-2*sqrt(2))^(1+n)+5*(3+2*sqrt(2))^(1+n))/4 for n>=0. - Colin Barker, Nov 04 2016

Mathematica

LinearRecurrence[{5, 5, -1}, {2, 8, 42}, 50] (* G. C. Greubel, Sep 27 2018 *)

Prog

(PARI) Vec(2*x^-1*(1-x-4*x^2)/((1+x)*(1-6*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 04 2016
(Magma) I:=[2, 8, 42]; [n le 3 select I[n] else 5*Self(n-1) + 5*Self(n-2) - Self(n-3): n in [1..30]]; // G. C. Greubel, Sep 27 2018

Crossrefs

Sequence in context: A357402 A129277 A120916 * A235350 A100327 A018934

Adjacent sequences: A133414 A133415 A133416 * A133418 A133419 A133420

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 27 2007

Status

approved