cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A006492 Generalized Lucas numbers.

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%I A006492 M3751 #32 Jul 08 2025 16:48:17
%S A006492 1,0,5,6,21,40,93,190,396,796,1586,3108,6025,11552,21947,41346,77311,
%T A006492 143580,265013,486398,888122,1613944,2920100,5261880,9445905,16897328,
%U A006492 30127665,53552190,94915273,167771168,295794125,520254094,912962120,1598652948
%N A006492 Generalized Lucas numbers.
%D A006492 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006492 Vincenzo Librandi, <a href="/A006492/b006492.txt">Table of n, a(n) for n = 3..1000</a>
%H A006492 L. Carlitz and R. Scoville, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-3/carlitz1.pdf">Zero-one sequences and Fibonacci numbers</a>, Fibonacci Quarterly, 15 (1977), 246-254.
%H A006492 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A006492 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%F A006492 G.f.: [(1-x)^2(1-2x+2x^2)]/[(1-x-x^2)^4]. - _Ralf Stephan_, Apr 23 2004
%p A006492 A006492:=(1-2*z+2*z**2)*(z-1)**2/(z**2+z-1)**4; # _Simon Plouffe_ in his 1992 dissertation.
%t A006492 CoefficientList[Series[(1 - x)^2 (1 - 2 x + 2 x^2) / (1 - x - x^2)^4, {x, 0, 33}], x] (* _Vincenzo Librandi_, Apr 26 2017 *)
%K A006492 nonn
%O A006492 3,3
%A A006492 _N. J. A. Sloane_