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Generalized Lucas numbers.
(Formerly M3751)
4

%I M3751 #26 Apr 13 2022 13:25:18

%S 1,0,5,6,21,40,93,190,396,796,1586,3108,6025,11552,21947,41346,77311,

%T 143580,265013,486398,888122,1613944,2920100,5261880,9445905,16897328,

%U 30127665,53552190,94915273,167771168,295794125,520254094,912962120,1598652948

%N Generalized Lucas numbers.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A006492/b006492.txt">Table of n, a(n) for n = 3..1000</a>

%H L. Carlitz and R. Scoville, <a href="http://www.fq.math.ca/Scanned/15-3/carlitz1.pdf">Zero-one sequences and Fibonacci numbers</a>, Fibonacci Quarterly, 15 (1977), 246-254.

%H 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 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%F G.f.: [(1-x)^2(1-2x+2x^2)]/[(1-x-x^2)^4]. - _Ralf Stephan_, Apr 23 2004

%p A006492:=(1-2*z+2*z**2)*(z-1)**2/(z**2+z-1)**4; # _Simon Plouffe_ in his 1992 dissertation.

%t 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 nonn

%O 3,3

%A _N. J. A. Sloane_.