A022530 Nexus numbers (n+1)^14 - n^14.

1, 16383, 4766585, 263652487, 5835080169, 72260648471, 599858908753, 3719823438255, 18478745943857, 77123207545039, 279749833583241, 904168630965623, 2653457921150425, 7174630439858727, 18080919199832609, 42864668012537311, 96320232521472993, 206435541022680095

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=13 of A047969.

Cf. A010802 (n^14).

Programs

Magma

[(n+1)^14 - n^14: n in [0..20]]; // G. C. Greubel, Feb 27 2018

Maple

b:=14: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # Muniru A Asiru, Feb 28 2018

Mathematica

Last[#]-First[#]&/@Partition[Range[0,20]^14,2,1] (* Harvey P. Dale, Oct 04 2011 *)
Table[(n+1)^14 - n^14, {n,0,20}] (* G. C. Greubel, Feb 27 2018 *)

PARI

for(n=0,20, print1((n+1)^14 - n^14, ", ")) \\ G. C. Greubel, Feb 27 2018

Formula

G.f.: (1+x) *(x^12 +16368*x^11 +4520946*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +4520946*x^2 +16368*x+1) / (x-1)^14 . - R. J. Mathar, Sep 02 2016

a(n) = A010802(n+1) - A010802(n). - Michel Marcus, Feb 28 2018