A133034 First differences of Padovan sequence A000931.

-1, 0, 1, -1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396

Offset: 0

Author

Omar E. Pol, Nov 05 2007

Keywords

• easy
• sign

Links

• Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.
• Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Crossrefs

The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.

Cf. A002026.

Programs

Mathematica

LinearRecurrence[{0,1,1},{-1,0,1},60] (* Harvey P. Dale, Dec 14 2013 *)

Formula

a(n+4) = A000931(n).

G.f.: ( 1-2*x^2 ) / ( -1+x^2+x^3 ). - R. J. Mathar, Sep 11 2011

a(n) = a(n-2) + a(n-3) with a(0) = -1, a(1) = 0, a(2) = 1. - Taras Goy, Mar 24 2019