OFFSET
0,1
REFERENCES
Mohammad K. Azarian, Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 45, 2012, pp. 2221-2227.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..950
Index entries for linear recurrences with constant coefficients, signature (8,40,-60,-40,8,1).
FORMULA
a(n) = L(5*n) + 5*(-1)^n*L(3*n) + 10*L(n), L(n) = A000032, the Lucas numbers.
G.f.: (32-255*x-1045*x^2+960*x^3+235*x^4-x^5)/((1-x-x^2)*(1+4*x-x^2)* (1-11*x-x^2)). [T. Mansour, Australas. J. Comb. 30 (2004), 207] - R. J. Mathar, Oct 26 2008
MATHEMATICA
Table[LucasL[n]^5, {n, 0, 30}] (* or *) CoefficientList[Series[(32 - 255 x - 1045 x^2 + 960 x^3 + 235 x^4 - x^5)/((1-x-x^2)*(1+4*x-x^2)*(1-11*x- x^2)), {x, 0, 50}], x] (* G. C. Greubel, Dec 21 2017 *)
PROG
(Magma) [ Lucas(n)^5 : n in [0..120]]; // Vincenzo Librandi, Apr 14 2011
(PARI) a(n)=(fibonacci(n-1)+fibonacci(n+1))^5 \\ Charles R Greathouse IV, Jun 11 2015
(PARI) x='x+O('x^30); Vec((32-255*x-1045*x^2+960*x^3+235*x^4-x^5)/((1-x-x^2)*(1+4*x-x^2)* (1-11*x-x^2))) \\ G. C. Greubel, Dec 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Feb 03 2005
STATUS
approved