A022527 - OEIS

%I #53 Aug 06 2024 04:38:51

%S 1,2047,175099,4017157,44633821,313968931,1614529687,6612607849,

%T 22791125017,68618940391,185311670611,457696700077,1049152023349,

%U 2257404775627,4600190689711,8942430185041,16679710263217,29996513771599,52221848818987,88309741101781

%N Nexus numbers: a(n) = (n+1)^11 - n^11.

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

%H T. D. Noe, <a href="/A022527/b022527.txt">Table of n, a(n) for n = 0..1000</a>

%H H. D. Nguyen, D. Taggart, <a href="https://citeseerx.ist.psu.edu/pdf/8f2f36f22878c984775ed04368b8893879b99458">Mining the OEIS: Ten Experimental Conjectures</a>, 2013. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F 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

%F a(n) = A008455(n+1) - A008455(n). - _Michel Marcus_, Feb 28 2018

%F 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

%p b:=11: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # _Muniru A Asiru_, Feb 28 2018

%t q=11; Table[(n+1)^q-n^q, {n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 23 2009 *)

%t Differences[Range[0, 20]^11] (* _Harvey P. Dale_, Jan 25 2011 *)

%o (Magma) [(n+1)^11-n^11: n in [0..40]]; // _Vincenzo Librandi_, Jan 26 2011

%o (PARI) for(n=0,20, print1((n+1)^11 - n^11, ", ")) \\ _G. C. Greubel_, Feb 27 2018

%Y Column k=10 of A047969.

%Y Cf. A008455 (n^11).

%Y Cf. A008292, A022526, A022538.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_