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

Author

Paul Curtz, Feb 07 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000032, A000045, A014217.

Programs

Magma

[4*Lucas(n): n in [0..30]]; // G. C. Greubel, Dec 21 2017

Mathematica

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

PARI

a(n)=4*(fibonacci(n-1)+fibonacci(n+1)) \\ Charles R Greathouse IV, Oct 16 2015

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.

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