A022523 Nexus numbers (n+1)^7-n^7.

1, 127, 2059, 14197, 61741, 201811, 543607, 1273609, 2685817, 5217031, 9487171, 16344637, 26916709, 42664987, 65445871, 97576081, 141903217, 201881359, 281651707, 386128261, 521088541, 693269347, 910467559, 1181645977, 1517044201, 1928294551, 2428543027

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
• H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; citseerx. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

First differences of A001015.

Cf. A008292, A022522, A022524.

Column k=6 of array A047969.

Programs

Magma

[(n+1)^7-n^7: n in [0..30]]; // Vincenzo Librandi, Nov 22 2011

Mathematica

q=7;lst={};Do[AppendTo[lst,(n+1)^q-n^q],{n,0,3*4!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 23 2009 *)
Table[(n+1)^7-n^7,{n,0,20}] (* Vincenzo Librandi, Nov 22 2011 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,127,2059,14197,61741,201811,543607},30] (* Harvey P. Dale, Apr 17 2017 *)
Differences[Range[0,50]^7] (* Harvey P. Dale, Jun 07 2023 *)

PARI

a(n)=(n+1)^7-n^7 \\ Charles R Greathouse IV, Sep 28 2015

Formula

G.f.: -(x^6+120*x^5+1191*x^4+2416*x^3+1191*x^2+120*x+1) / (x-1)^7. - Colin Barker, Dec 21 2012

G.f.: polylog(-7, x)*(1-x)/x. See the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021