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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: A134203 A014777 A221193 * A221760 A037932 A285417

Adjacent sequences:  A103322 A103323 A103324 * A103326 A103327 A103328

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Feb 03 2005

STATUS

approved

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Last modified February 23 23:56 EST 2018. Contains 299595 sequences. (Running on oeis4.)