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A088859 a(n) = L(n) + 2^n where L(n) = A000032(n) (the Lucas numbers). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

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

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 A116880 A051123

Adjacent sequences:  A088856 A088857 A088858 * A088860 A088861 A088862

KEYWORD

easy,nonn

AUTHOR

Miklos Kristof, Nov 25 2003

STATUS

approved

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Last modified June 13 13:40 EDT 2021. Contains 344999 sequences. (Running on oeis4.)