A138034 Expansion of (1+3*x^2)/(1-x+x^2).

1, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3, 2, -1, -3, -2, 1, 3

Offset: 0

Author

Karem Boubaker (mmbb11112000(AT)yahoo.fr), Mar 01 2008; corrected Mar 03 2008

Keywords

• sign
• easy

Comments

Essentially a duplicate of A119910: 1, followed by A119910. - Joerg Arndt, Nov 14 2014

Links

• Karem Boubaker and Lin Zhang, Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis, arXiv preprint arXiv:1203.2082, 2012. - From _N. J. A. Sloane_, Sep 15 2012
• Index entries for linear recurrences with constant coefficients, signature (1,-1).

Crossrefs

Cf. A135929, A135936, A137276.

Programs

Mathematica

CoefficientList[Series[(1 + 3*x^2)/(1 - x + x^2), {x, 0, 100}], x] (* Wesley Ivan Hurt, Jan 15 2017 *)
LinearRecurrence[{1,-1},{1,1,3},120] (* Harvey P. Dale, Jun 14 2024 *)

Formula

a(n) = A119910(n), n>=1.

G.f.: (1+3*x^2)/(1-x+x^2). a(n)=a(n-1)-a(n-2), n>2.