A006492 Generalized Lucas numbers.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Programs

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 *)

Formula

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