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 A099923 Fourth powers of Lucas numbers A000032. 6
 16, 1, 81, 256, 2401, 14641, 104976, 707281, 4879681, 33362176, 228886641, 1568239201, 10750371856, 73680216481, 505022001201, 3461445366016, 23725169980801, 162614549665681, 1114577187760656, 7639424429247601 (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. A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 56. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,15,-15,-5,1). FORMULA a(n) = (A000032(n))^4 = (A001254(n))^2. a(n) = L(4*n) + 4*(-1)^n*L(2*n) + 6. a(n) = L(n-2)*L(n-1)*L(n+1)*L(n+2) + 25, for n >=1. G.f.: (16-79*x-164*x^2+76*x^3+x^4)/((1-x)*(1+3*x+x^2)*(1-7*x+x^2)). [T. Mansour, Australas. J. Combin. 30 (2004), 207] - R. J. Mathar, Oct 26 2008 a(0)=16, a(1)=1, a(2)=81, a(3)=256, a(4)=2401, a(n) = 5*a(n-1) + 15*a(n-2) - 15*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Jul 04 2014 MATHEMATICA LucasL[Range[0, 20]]^4 (* or *) LinearRecurrence[{5, 15, -15, -5, 1}, {16, 1, 81, 256, 2401}, 21] (* Harvey P. Dale, Jul 04 2014 *) CoefficientList[Series[(16 - 79 x - 164 x^2 + 76 x^3 + x^4)/((1 - x) (1 + 3*x+x^2)*(1-7*x+x^2)), {x, 0, 50}], x] (* G. C. Greubel, Dec 21 2017 *) PROG (MAGMA) [ Lucas(n)^4 : n in [0..120]]; // Vincenzo Librandi, Apr 14 2011 (PARI) for(n=0, 30, print1( (fibonacci(n+1) + fibonacci(n-1))^4, ", ")) \\ G. C. Greubel, Dec 21 2017 (PARI) x='x+O('x^30); Vec((16-79*x-164*x^2+76*x^3+x^4)/((1-x)*(1+3*x+x^2)*(1-7*x+x^2))) \\ G. C. Greubel, Dec 21 2017 CROSSREFS Cf. A075515. Fourth row of array A103324. Sequence in context: A040271 A036179 A309132 * A105671 A145828 A223518 Adjacent sequences:  A099920 A099921 A099922 * A099924 A099925 A099926 KEYWORD nonn AUTHOR Ralf Stephan, Nov 01 2004 STATUS approved

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)