A022523 - OEIS

%I #37 Aug 06 2024 04:35:18

%S 1,127,2059,14197,61741,201811,543607,1273609,2685817,5217031,9487171,

%T 16344637,26916709,42664987,65445871,97576081,141903217,201881359,

%U 281651707,386128261,521088541,693269347,910467559,1181645977,1517044201,1928294551,2428543027

%N Nexus numbers (n+1)^7-n^7.

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

%H Vincenzo Librandi, <a href="/A022523/b022523.txt">Table of n, a(n) for n = 0..10000</a>

%H H. D. Nguyen, D. Taggart, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/nguyen/talks/Ten_Experimental_Conjectures_JMM_2013.pdf">Mining the OEIS: Ten Experimental Conjectures</a>, 2013; <a href="http://citeseerx.ist.psu.edu/pdf/8f2f36f22878c984775ed04368b8893879b99458">citseerx</a>. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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

%F 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

%t q=7;lst={};Do[AppendTo[lst,(n+1)^q-n^q],{n,0,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 23 2009 *)

%t Table[(n+1)^7-n^7,{n,0,20}] (* _Vincenzo Librandi_, Nov 22 2011 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,127,2059,14197,61741,201811,543607},30] (* _Harvey P. Dale_, Apr 17 2017 *)

%t Differences[Range[0,50]^7] (* _Harvey P. Dale_, Jun 07 2023 *)

%o (Magma) [(n+1)^7-n^7: n in [0..30]]; // _Vincenzo Librandi_, Nov 22 2011

%o (PARI) a(n)=(n+1)^7-n^7 \\ _Charles R Greathouse IV_, Sep 28 2015

%Y First differences of A001015.

%Y Cf. A008292, A022522, A022524.

%Y Column k=6 of array A047969.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_