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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, 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]

MATHEMATICA

Table[n^4-1, {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)

PROG

(MAGMA) [n^4 - 1: n in [1..50]]; // Vincenzo Librandi, May 01 2011

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 August 21 23:28 EDT 2017. Contains 290940 sequences.