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A103325
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Fifth powers of Lucas numbers.
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5
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32, 1, 243, 1024, 16807, 161051, 1889568, 20511149, 229345007, 2535525376, 28153056843, 312079600999, 3461619737632, 38387392786601, 425733547012443, 4721411479245824, 52361450147627807
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OFFSET
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0,1
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REFERENCES
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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.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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