A022528 Nexus numbers (n+1)^12-n^12.

1, 4095, 527345, 16245775, 227363409, 1932641711, 11664504865, 54878189535, 213710059745, 717570463519, 2138428376721, 5777672071535, 14381984674225, 33395827252815, 73052425515329, 151728638820031, 301147260519105, 574209144196415

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Column k=11 of array A047969.

Cf. A008292, A022527, A022529.

Programs

Magma

[(n+1)^12-n^12: n in [0..20]]; // Vincenzo Librandi, Nov 22 2011

Mathematica

lst={};Do[a=n^6;b=(n+1)^6;s=(a+b)*(b-a);AppendTo[lst,s],{n,0,4!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 23 2009 *)
Table[(n+1)^12-n^12,{n,0,20}] (* Vincenzo Librandi, Nov 22 2011 *)
LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,4095,527345,16245775,227363409,1932641711,11664504865,54878189535,213710059745,717570463519,2138428376721,5777672071535},20] (* Harvey P. Dale, Apr 23 2019 *)

PARI

vector(30, n, n--; (n+1)^12-n^12) \\ Colin Barker, Nov 30 2014

Formula

a(n) = A008456(n+1) - A008456(n). - Colin Barker, Nov 30 2014

G.f.: (x +1)*(x^10 +4082*x^9 +474189*x^8 +9713496*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 +9713496*x^3 +474189*x^2 +4082*x +1) / (x -1)^12. - Colin Barker, Nov 30 2014

G.f.: polylog(-12, 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