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A103325 Fifth powers of Lucas numbers. 5

%I

%S 32,1,243,1024,16807,161051,1889568,20511149,229345007,2535525376,

%T 28153056843,312079600999,3461619737632,38387392786601,

%U 425733547012443,4721411479245824,52361450147627807

%N Fifth powers of Lucas numbers.

%D 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.

%H G. C. Greubel, <a href="/A103325/b103325.txt">Table of n, a(n) for n = 0..950</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,40,-60,-40,8,1).

%F a(n) = (A000032(n))^5 = A000032(n)*A099923(n).

%F a(n) = L(5*n) + 5*(-1)^n*L(3*n) + 10*L(n), L(n) = A000032, the Lucas numbers.

%F 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

%t 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 *)

%o (MAGMA) [ Lucas(n)^5 : n in [0..120]]; // _Vincenzo Librandi_, Apr 14 2011

%o (PARI) a(n)=(fibonacci(n-1)+fibonacci(n+1))^5 \\ _Charles R Greathouse IV_, Jun 11 2015

%o (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

%Y Fifth row of array A103325.

%K nonn,easy

%O 0,1

%A _Ralf Stephan_, Feb 03 2005

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Last modified June 6 17:33 EDT 2020. Contains 334831 sequences. (Running on oeis4.)