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A022528
Nexus numbers (n+1)^12-n^12.
5
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
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.
Sequence in context: A326383 A160972 A038999 * A024010 A123868 A321557
KEYWORD
nonn,easy
STATUS
approved