A022527 Nexus numbers: a(n) = (n+1)^11 - n^11.
1, 2047, 175099, 4017157, 44633821, 313968931, 1614529687, 6612607849, 22791125017, 68618940391, 185311670611, 457696700077, 1049152023349, 2257404775627, 4600190689711, 8942430185041, 16679710263217, 29996513771599, 52221848818987, 88309741101781
Offset: 0
References
- J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
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Magma
[(n+1)^11-n^11: n in [0..40]]; // Vincenzo Librandi, Jan 26 2011
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Maple
b:=11: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # Muniru A Asiru, Feb 28 2018
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Mathematica
q=11; Table[(n+1)^q-n^q, {n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Jan 23 2009 *) Differences[Range[0, 20]^11] (* Harvey P. Dale, Jan 25 2011 *) -
PARI
for(n=0,20, print1((n+1)^11 - n^11, ", ")) \\ G. C. Greubel, Feb 27 2018
Formula
G.f.: -(x^10 + 2036*x^9 + 152637*x^8 + 2203488*x^7 + 9738114*x^6 + 15724248*x^5 + 9738114*x^4 + 2203488*x^3 + 152637*x^2 + 2036*x + 1) / (x - 1)^11. - Colin Barker, Dec 22 2012
G.f.: polylog(-11, x)*(1-x)/x. See the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021