A166977 Jacobsthal-Lucas numbers A014551, except a(0) = 0.

0, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, 2047, 4097, 8191, 16385, 32767, 65537, 131071, 262145, 524287, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911, 1073741825, 2147483647

Offset: 0

Author

Paul Curtz, Oct 26 2009

Keywords

• nonn
• less
• easy

Comments

The sequence (-1)^n*a(n) is the inverse binomial transform of A166956.

The main diagonal of the table of a(n) and its higher differences in successive rows is 0,4,8,16,32,.. , 4*A131577(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Programs

Mathematica

Join[{0, 1}, LinearRecurrence[{1, 2}, {5, 7}, 50]] (* or *) Table[2^n + (-1)^n, {n,1,25}] (* G. C. Greubel, May 30 2016 *)

Formula

a(n) = A014551(n), n>0.

a(n) - A001045(n) = A097073(n), n>0.

a(n) - A001045(n) = 4*A001045(n-1).

a(n) = a(n-1) + 2*a(n-2), n>2.

G.f.: x*(1 + 4*x)/((1+x) * (1-2*x)).

a(n) = (-1)^n + 2^n for n>0. - Colin Barker, Jun 06 2012

E.g.f.: exp(2*x) + exp(-x) - 2. - G. C. Greubel, May 30 2016

Extensions

Edited and extended by R. J. Mathar, Mar 14 2010