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%I M5198 #37 Apr 13 2022 13:25:18
%S 1,28,92,435,1766,7598,31987,135810,574786,2435653,10316252,43702500,
%T 185123261,784200368,3321916912,14071880655,59609419066,252509590018,
%U 1069647725567,4531100578950,19194049901126,81307300410353
%N Partial sums of cubes of Lucas numbers.
%D A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 21.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A005971/b005971.txt">Table of n, a(n) for n = 1..1000</a>
%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+24*x-23*x^2-8*x^3)/((1-x)*(1+x-x^2)*(1-4*x-x^2)). - _Ralf Stephan_, Apr 23 2004
%F a(n) = A000032(3*n+2)/2+3*(-1)^n*A000032(n-1)+3/2. - _Vaclav Kotesovec_, Nov 19 2012
%p lucas := proc(n) option remember: if n=1 then RETURN(1) fi: if n=2 then RETURN(3) fi: lucas(n-1)+lucas(n-2) end: l[0] := 0: for i from 1 to 50 do l[i] := l[i-1]+lucas(i)^3; printf(`%d,`,l[i]) od: # _James A. Sellers_, May 29 2000
%p A005971:=(-1-24*z+23*z**2+8*z**3)/(z-1)/(z**2+4*z-1)/(z**2-z-1); # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t Table[LucasL[3*n+2]/2+3*(-1)^n*LucasL[n-1]+3/2,{n,1,20}] (* _Vaclav Kotesovec_, Nov 19 2012 *)
%t CoefficientList[Series[(1 + 24 x - 23 x^2 - 8 x^3) / ((1-x) (1+x-x^2) (1-4*x-x^2)), {x, 0, 30}], x] (* _Vincenzo Librandi_, May 03 2013 *)
%t Accumulate[LucasL[Range[30]]^3] (* _Harvey P. Dale_, Oct 11 2021 *)
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, May 29 2000
%E Definition clarified by _Harvey P. Dale_, Oct 11 2021
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