A022529 Nexus numbers (n+1)^13-n^13.

1, 8191, 1586131, 65514541, 1153594261, 11839990891, 83828316391, 452866803481, 1992110014441, 7458134171671, 24522712143931, 72470493235141, 195881901213181, 490839666661891, 1152480295105231, 2557404559011121, 5400978405535441, 10918386832765231

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Column k=12 of array A047969.

Cf. A008292, A022528.

Programs

Magma

[(n+1)^13-n^13: n in [0..20]]; // Vincenzo Librandi, Nov 22 2011

Mathematica

q=13;lst={};Do[AppendTo[lst,(n+1)^q-n^q],{n,0,4!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 23 2009 *)
Table[(n+1)^13-n^13,{n,0,20}] (* Vincenzo Librandi, Nov 22 2011 *)

PARI

a(n) = (n+1)^13 - n^13; \\ Michel Marcus, Sep 25 2014

Formula

a(n) = A010801(n+1) - A010801(n). - Michel Marcus, Sep 25 2014

G.f.: -(x^12 +8178*x^11 +1479726*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +1479726*x^2 +8178*x +1) / (x-1)^13. - Colin Barker, Sep 25 2014

G.f.: polylog(-13, x)*(1-x)/x. See the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021