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%I #21 Dec 07 2019 12:18:25
%S 1,14,181,2339,30226,390599,5047561,65227694,842912461,10892634299,
%T 140761333426,1819004700239,23506299769681,303762892305614,
%U 3925411300203301,50726584010337299,655520180834181586,8471035766834023319,109467944788008121561
%N a(n) = 13*a(n-1) - a(n-2).
%H Harvey P. Dale, <a href="/A126866/b126866.txt">Table of n, a(n) for n = 0..899</a>
%H Alex Fink, Richard K. Guy, and Mark Krusemeyer, <a href="https://doi.org/10.11575/cdm.v3i2.61940">Partitions with parts occurring at most thrice</a>, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114. See Section 13.
%H Andersen, K., Carbone, L. and Penta, D., <a href="https://pdfs.semanticscholar.org/8f0c/c3e68d388185129a56ed73b5d21224659300.pdf">Kac-Moody Fibonacci sequences, hyperbolic golden ratios, and real quadratic fields</a>, Journal of Number Theory and Combinatorics, Vol 2, No. 3 pp 245-278, 2011. See Section 9.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13, -1).
%F a(n) = 13*a(n-1) - a(n-2); a(0)=1, a(1)=14.
%F G.f.: (x+1)/(x^2-13*x+1). - _Harvey P. Dale_, Mar 28 2013
%t LinearRecurrence[{13,-1},{1,14},30] (* _Harvey P. Dale_, Mar 28 2013 *)
%o (Sage) [(lucas_number2(n,13,1)-lucas_number2(n-1,13,1))/11 for n in range(1, 16)] # _Zerinvary Lajos_, Nov 10 2009
%Y Cf. A002878, A001834, A030221, A002315.
%K easy,nonn
%O 0,2
%A Diego A. Penta (diego(AT)alum.mit.edu), Mar 15 2007
%E Corrected and extended by _Harvey P. Dale_, Mar 28 2013
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