A060182 a(0) = 1, a(1) = 5, a(2) = 13; a(n) = 2*a(n-1) + 2, n > 2.

1, 5, 13, 28, 58, 118, 238, 478, 958, 1918, 3838, 7678, 15358, 30718, 61438, 122878, 245758, 491518, 983038, 1966078, 3932158, 7864318, 15728638, 31457278, 62914558, 125829118, 251658238, 503316478, 1006632958, 2013265918

Offset: 0

Author

Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), Mar 19 2001

Keywords

• nonn
• easy

Comments

Sometimes confused with A002717.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (3, -2).

Programs

PARI

{ a=-1; for (n=0, 200, a=2*a + 2; if (n<3, a++); write("b060182.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 02 2009

Formula

a(n) = 3(a(n-1) - a(n-2) + a(n-3) - ... ((-1)^(n+1))*a(0))+1;

a(n) = (2^(n-3))*a(3) + (2^(n-2)) - 2 for n > 3.

From R. J. Mathar, Jul 15 2009: (Start)

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

a(n) = 15*2^(n-2) - 2, n > 1. (End)

Extensions

Simpler formula and more terms from Larry Reeves (larryr(AT)acm.org), Mar 30 2001

Edited by N. J. A. Sloane at the suggestion of Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Sep 16 2007