The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A103325 Fifth powers of Lucas numbers. 5
 32, 1, 243, 1024, 16807, 161051, 1889568, 20511149, 229345007, 2535525376, 28153056843, 312079600999, 3461619737632, 38387392786601, 425733547012443, 4721411479245824, 52361450147627807 (list; graph; refs; listen; history; text; internal format)
 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 * A221760 A037932 A285417 Adjacent sequences:  A103322 A103323 A103324 * A103326 A103327 A103328 KEYWORD nonn,easy AUTHOR Ralf Stephan, Feb 03 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 17:58 EDT 2020. Contains 333127 sequences. (Running on oeis4.)