A156279 4 times the Lucas number A000032(n).

8, 4, 12, 16, 28, 44, 72, 116, 188, 304, 492, 796, 1288, 2084, 3372, 5456, 8828, 14284, 23112, 37396, 60508, 97904, 158412, 256316, 414728, 671044, 1085772, 1756816, 2842588, 4599404, 7441992

Offset

0,1

Comments

This is a second kind "autosequence" whose first kind companion is A022087. - Jean-François Alcover, Aug 20 2022

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

OEIS Wiki, Autosequence

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

Formula

a(n) = 4*A000032(n).

a(n) = a(n-1) + a(n-2).

a(n) = A014217(n+3) - A014217(n-3), with A014217(-5) = -11, A014217(-4) = 6, A014217(-3) = -4, A014217(-2) = 2, A014217(-1) = -1 extended as proposed in A153263.

a(n) = 4*((1/2) + (1/2)*sqrt(5))^n + 4*((1/2) - (1/2)*sqrt(5))^n. - Paolo P. Lava, Feb 13 2009

G.f. 4*(-2 + x) / (-1 + x + x^2). - R. J. Mathar, Mar 11 2011

a(n) = Lucas(n+3) - Lucas(n-3), where Lucas(i) for i = 0..2 gives -4, 3, -1. - Bruno Berselli, Jul 27 2017

Mathematica

Table[4*LucasL[n], {n, 0, 30}] (* G. C. Greubel, Dec 21 2017 *)

Prog

(PARI) a(n)=4*(fibonacci(n-1)+fibonacci(n+1)) \\ Charles R Greathouse IV, Oct 16 2015
(Magma) [4*Lucas(n): n in [0..30]]; // G. C. Greubel, Dec 21 2017

Crossrefs

Cf. A000032, A000045, A014217.

Sequence in context: A239971 A082073 A244209 * A203072 A131873 A220130

Adjacent sequences: A156276 A156277 A156278 * A156280 A156281 A156282

Keyword

nonn,easy

Author

Paul Curtz, Feb 07 2009

Status

approved