|
%I M4063 #29 Apr 13 2022 13:25:18
%S 1,0,6,7,28,54,135,286,627,1313,2730,5565,11212,22304,43911,85614,
%T 165490,317373,604296,1143054,2149074,4017950,7473180,13832910,
%U 25490115,46774448,85494900,155693873,282551856,511101624,921676437,1657238030,2971622493,5314551351
%N Generalized Lucas numbers.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%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. has denominator (1 - x - x^2)^5.
%p A006493:=(1-2*z+2*z**2)*(z-1)**3/(z**2+z-1)**5; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%p 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
%t 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 *)
%K nonn
%O 3,3
%A _N. J. A. Sloane_
|
