A153263 a(n) = A014217(n+3) - A014217(n).

3, 5, 9, 13, 23, 35, 59, 93, 153, 245, 399, 643, 1043, 1685, 2729, 4413, 7143, 11555, 18699, 30253, 48953, 79205, 128159, 207363, 335523, 542885, 878409, 1421293, 2299703, 3720995, 6020699, 9741693, 15762393, 25504085, 41266479, 66770563

Offset: 0

Author

Paul Curtz, Dec 22 2008

Keywords

• nonn
• easy

Comments

The least significant digits are a sequence of period length 4: 3,5,9,3.

One could extend A014217 using its recurrence to define A014217(-1)=-1. This would add a(-1)=3 here by definition, and the least significant digits would still follow the (same, wrapped) period of length 4: 3,3,5,9.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Crossrefs

Cf. A022112.

Programs

Mathematica

LinearRecurrence[{0,2,1},{3,5,9},40] (* Harvey P. Dale, Jun 23 2022 *)

Formula

a(2n+2) = a(2n+1) + a(2n) + 1. a(2n+3) = a(2n+2) + a(2n+1) - 1.

From R. J. Mathar, Feb 07 2009, Apr 18 2009: (Start)

a(n) = 2*a(n-2) + a(n-3) = (-1)^n + 2*A000032(n+1).

G.f.: (3+5x+3x^2)/ ((1+x)(1-x-x^2)). (End)

a(n) + a(n+1) = A022112(n+2). - R. J. Mathar, Feb 25 2013

a(n) = ((-2)^n + (1 - sqrt(5))^(1+n) + (1 + sqrt(5))^(1+n))/2^n. - Stefano Spezia, Dec 25 2021

Extensions

More terms from R. J. Mathar, Feb 07 2009

Edited by R. J. Mathar, Apr 18 2009