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
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).
Programs
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Magma
[(n+1)^8-n^8: n in [0..30]]; // Vincenzo Librandi, Nov 22 2011
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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 *) -
PARI
a(n)=(n+1)^8-n^8 \\ Charles R Greathouse IV, Oct 07 2015
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
Extensions
More terms from Stefan Steinerberger, Apr 09 2006
More terms from Colin Barker, Dec 21 2012