A022524 Nexus numbers (n+1)^8 - n^8.

1, 255, 6305, 58975, 325089, 1288991, 4085185, 11012415, 26269505, 56953279, 114358881, 215622815, 385749025, 660058335, 1087101569, 1732076671, 2680790145, 4044203135, 5963602465, 8616436959, 12222859361, 17053014175, 23435111745, 31764328895, 42512576449

Offset

0,2

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 (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: (x+1)*(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1) / (x-1)^8. - Colin Barker, Dec 21 2012

G.f.: polylog(-8, x)*(1-x)/x. See the g.f. of Colin Barker (with expanded numerator), and the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021

Mathematica

Table[(n + 1)^8 - n^8, {n, 0, 25}] (* Stefan Steinerberger, Apr 09 2006 *)
Last[#]-First[#]&/@Partition[Range[0, 30]^8, 2, 1] (* Harvey P. Dale, Nov 24 2013 *)
Differences[Range[0, 30]^8] (* Harvey P. Dale, Sep 24 2021 *)

Prog

(Magma) [(n+1)^8-n^8: n in [0..30]]; // Vincenzo Librandi, Nov 22 2011
(PARI) a(n)=(n+1)^8-n^8 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Column k=7 of array A047969.

Cf. A008292, A022523, A022525.

Sequence in context: A181127 A228264 A228223 * A261032 A069093 A024006

Adjacent sequences: A022521 A022522 A022523 * A022525 A022526 A022527

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Stefan Steinerberger, Apr 09 2006

More terms from Colin Barker, Dec 21 2012

Status

approved