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A006493 Generalized Lucas numbers.
(Formerly M4063)
2
1, 0, 6, 7, 28, 54, 135, 286, 627, 1313, 2730, 5565, 11212, 22304, 43911, 85614, 165490, 317373, 604296, 1143054, 2149074, 4017950, 7473180, 13832910, 25490115, 46774448, 85494900, 155693873, 282551856, 511101624, 921676437, 1657238030, 2971622493, 5314551351 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

REFERENCES

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

LINKS

Table of n, a(n) for n=3..36.

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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

G.f. has denominator (1 - x - x^2)^5.

MAPLE

A006493:=(1-2*z+2*z**2)*(z-1)**3/(z**2+z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation

a:= n-> (Matrix([[7, 6, 0, 1, 0$4, -2, 18]]). Matrix(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [5, -5, -10, 15, 11, -15, -10, 5, 5, 1][i] else 0 fi)^n)[1, 7]: seq (a(n), n=3..36); # Alois P. Heinz, Aug 26 2008

MATHEMATICA

CoefficientList[(1-x)^3*(1-2*x+2*x^2)/(1-x-x^2)^5 + O[x]^40, x] (* Jean-François Alcover, May 29 2015 *)

CROSSREFS

Sequence in context: A042419 A037956 A095369 * A292106 A037375 A159582

Adjacent sequences:  A006490 A006491 A006492 * A006494 A006495 A006496

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 19 22:00 EDT 2018. Contains 316378 sequences. (Running on oeis4.)