A126866 a(n) = 13*a(n-1) - a(n-2).

1, 14, 181, 2339, 30226, 390599, 5047561, 65227694, 842912461, 10892634299, 140761333426, 1819004700239, 23506299769681, 303762892305614, 3925411300203301, 50726584010337299, 655520180834181586, 8471035766834023319, 109467944788008121561

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..899

Alex Fink, Richard K. Guy, and Mark Krusemeyer, Partitions with parts occurring at most thrice, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114. See Section 13.

Andersen, K., Carbone, L. and Penta, D., Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields, Journal of Number Theory and Combinatorics, Vol 2, No. 3 pp 245-278, 2011. See Section 9.

Index entries for linear recurrences with constant coefficients, signature (13, -1).

Formula

a(n) = 13*a(n-1) - a(n-2); a(0)=1, a(1)=14.

G.f.: (x+1)/(x^2-13*x+1). - Harvey P. Dale, Mar 28 2013

Mathematica

LinearRecurrence[{13, -1}, {1, 14}, 30] (* Harvey P. Dale, Mar 28 2013 *)

Prog

(Sage) [(lucas_number2(n, 13, 1)-lucas_number2(n-1, 13, 1))/11 for n in range(1, 16)] # Zerinvary Lajos, Nov 10 2009

Crossrefs

Cf. A002878, A001834, A030221, A002315.

Sequence in context: A274565 A125471 A132010 * A230055 A133286 A163416

Adjacent sequences: A126863 A126864 A126865 * A126867 A126868 A126869

Keyword

easy,nonn

Author

Diego A. Penta (diego(AT)alum.mit.edu), Mar 15 2007

Extensions

Corrected and extended by Harvey P. Dale, Mar 28 2013

Status

approved