A006492 Generalized Lucas numbers. (Formerly M3751)

1, 0, 5, 6, 21, 40, 93, 190, 396, 796, 1586, 3108, 6025, 11552, 21947, 41346, 77311, 143580, 265013, 486398, 888122, 1613944, 2920100, 5261880, 9445905, 16897328, 30127665, 53552190, 94915273, 167771168, 295794125, 520254094, 912962120, 1598652948

Offset

3,3

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

L. Carlitz and R. Scoville, Zero-one sequences and Fibonacci numbers, Fibonacci Quarterly, 15 (1977), 246-254.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Formula

G.f.: [(1-x)^2(1-2x+2x^2)]/[(1-x-x^2)^4]. - Ralf Stephan, Apr 23 2004

Maple

A006492:=(1-2*z+2*z**2)*(z-1)**2/(z**2+z-1)**4; # Simon Plouffe in his 1992 dissertation.

Mathematica

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 *)

Crossrefs

Sequence in context: A037951 A095308 A132796 * A110344 A224915 A135301

Adjacent sequences: A006489 A006490 A006491 * A006493 A006494 A006495

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved