A088859 a(n) = L(n) + 2^n where L(n) = A000032(n) (the Lucas numbers).

3, 3, 7, 12, 23, 43, 82, 157, 303, 588, 1147, 2247, 4418, 8713, 17227, 34132, 67743, 134643, 267922, 533637, 1063703, 2121628, 4233907, 8452687, 16880898, 33722193, 67380307, 134656932, 269146103, 538020763, 1075602322, 2150493997

Offset

0,1

Comments

Lim_{n->infinity} a(n)/a(n-1) = 2.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (3, -1, -2).

Formula

G.f.: (3 - 6*x + 2*x^2) / (1 - 3*x + x^2 + 2*x^3)

a(n) = p^n + q^n + r^n, where p = (1+sqrt(5))/2, q = (1-sqrt(5))/2, and r = 2*p^n + q^n = L(n) = A000032(n), so a(n) = L(n) + 2^n

a(0)=3, a(1)=3, a(2)=7 and a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n >= 3.

Example

a(6) = 82 = L(6) + 2^6 = 18 + 64.
a(7) = 157 = 3*82 - 43 - 2*23 = 246 - 43 - 46.

Prog

(Magma) [2^n+Lucas(n): n in [0..50]]; // Vincenzo Librandi, Apr 14 2011

Crossrefs

Cf. A000032.

Sequence in context: A068626 A126698 A219211 * A177942 A360873 A116880

Adjacent sequences: A088856 A088857 A088858 * A088860 A088861 A088862

Keyword

easy,nonn

Author

Miklos Kristof, Nov 25 2003

Status

approved