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 A123865 a(n) = n^4 - 1. 18
 0, 15, 80, 255, 624, 1295, 2400, 4095, 6560, 9999, 14640, 20735, 28560, 38415, 50624, 65535, 83520, 104975, 130320, 159999, 194480, 234255, 279840, 331775, 390624, 456975, 531440, 614655, 707280, 809999, 923520, 1048575, 1185920, 1336335 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) mod 5 = 0 iff n mod 5 > 0: a(A008587(n)) = 4; a(A047201(n)) = 0; a(n) mod 5 = 4*(1-A079998(n)). A129292(n) = number of divisors of a(n) that are not greater than n. - Reinhard Zumkeller, Apr 09 2007 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: x^2*(15 + 5*x + 5*x^2 - x^3)/(1-x)^5. - Colin Barker, Jan 10 2012 -4*a(n+1) = -4*n*(n+2)*(n^2+2*n+2) = (n+n*i)*(n+2+n*i)*(n+(n+2)*i)*(n+2+(n+2)*i), where i is the imaginary unit. - Jon Perry, Feb 05 2014 From Vaclav Kotesovec, Feb 14 2015: (Start) Sum_{n>=2} 1/a(n) = 7/8 - Pi*coth(Pi)/4. Sum_{n>=2} (-1)^n / a(n) = 1/8 - Pi/(4*sinh(Pi)). (End) a(n) = A005563(A005563(n)). - Bruno Berselli, May 28 2015 E.g.f.: 1 + (-1 + x + 7*x^2 + 6*x^3 + x^4)*exp(x). - G. C. Greubel, Aug 08 2019 MAPLE seq(n^4 -1, n=1..40); # G. C. Greubel, Aug 08 2019 MATHEMATICA Table[n^4-1, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *) PROG (MAGMA) [n^4 - 1: n in [1..40]]; // Vincenzo Librandi, May 01 2011 (PARI) vector(40, n, n^4 -1) \\ G. C. Greubel, Aug 08 2019 (Sage) [n^4 -1 for n in (1..40)] # G. C. Greubel, Aug 08 2019 (GAP) List([1..40], n-> n^4 -1); # G. C. Greubel, Aug 08 2019 CROSSREFS Cf. A000583, A005563, A024002, A123866, A123867, A123868, A219086. Sequence in context: A180577 A033594 A059377 * A024002 A050149 A055815 Adjacent sequences:  A123862 A123863 A123864 * A123866 A123867 A123868 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, Oct 16 2006 STATUS approved

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Last modified October 15 17:22 EDT 2019. Contains 328033 sequences. (Running on oeis4.)