OFFSET
0,2
COMMENTS
Last digit of a(n) is always 1. Last two digits of a(n) (i.e., a(n) mod 100) are repeated periodically with palindromic part of period 20 {1,31,11,81,1,51,31,61,81,51,51,81,61,31,51,1,81,11,31,1}. Last three digits of a(n) (i.e., a(n) mod 1000) are repeated periodically with palindromic part of period 200. - Alexander Adamchuk, Aug 11 2006
In Conway and Guy, these numbers are called nexus numbers of order 5. - M. F. Hasler, Jan 27 2013
REFERENCES
John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Polytope Wiki, Triangular-antitegmatic Icosachoron
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (-1-x^4-26*x^3-66*x^2-26*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
G.f.: polylog(-5, x)*(1-x)/x. See the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021
Sum_{n>=0} 1/a(n) = c1*tanh(c2/2) - c2*tanh(c1/2), where c1 = tan(3*Pi/10)*Pi and c2 = tan(Pi/10)*Pi. - Amiram Eldar, Jan 27 2022
MATHEMATICA
Table[(n+1)^5-n^5, {n, 0, 30}] (* Vincenzo Librandi, Nov 23 2011 *)
PROG
(Magma) [(n+1)^5-n^5: n in [0..30]]; // Vincenzo Librandi, Nov 23 2011
(PARI) a(n)=(n+1)^5-n^5 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved