A103325 Fifth powers of Lucas numbers.

32, 1, 243, 1024, 16807, 161051, 1889568, 20511149, 229345007, 2535525376, 28153056843, 312079600999, 3461619737632, 38387392786601, 425733547012443, 4721411479245824, 52361450147627807

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) = (A000032(n))^5 = A000032(n)*A099923(n).

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

Fifth row of array A103325.

Sequence in context: A301910 A302154 A221193 * A351245 A221760 A037932

Adjacent sequences: A103322 A103323 A103324 * A103326 A103327 A103328

Keyword

nonn,easy

Author

Ralf Stephan, Feb 03 2005

Status

approved