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

0,2

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).

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 +56604978*x^6 +105907308*x^5 +56604978*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

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 *)

Prog

(Magma) [(n+1)^12-n^12: n in [0..20]]; // Vincenzo Librandi, Nov 22 2011
(PARI) vector(30, n, n--; (n+1)^12-n^12) \\ Colin Barker, Nov 30 2014

Crossrefs

Column k=11 of array A047969.

Cf. A008292, A022527, A022529.

Sequence in context: A326383 A160972 A038999 * A024010 A123868 A321557

Adjacent sequences: A022525 A022526 A022527 * A022529 A022530 A022531

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved