A022522 Nexus numbers (n+1)^6 - n^6.

1, 63, 665, 3367, 11529, 31031, 70993, 144495, 269297, 468559, 771561, 1214423, 1840825, 2702727, 3861089, 5386591, 7360353, 9874655, 13033657, 16954119, 21766121, 27613783, 34655985, 43067087, 53037649, 64775151, 78504713, 94469815, 112933017, 134176679

Offset: 0

Author

N. J. A. Sloane, Jun 14 1998

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
• Eric Weisstein's World of Mathematics, Nexus Number
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Column k=5 of array A047969.

Beginning with n=1, a subsequence of A181125 (difference of two positive 6th powers). - Mathew Englander, Jun 01 2014

Cf. A008292, A022521, A022523.

Programs

GAP

List([0..30], n-> (n+1)^6 - n^6); # G. C. Greubel, Aug 28 2019

Magma

[(n+1)^6-n^6: n in [0..30]]; // Vincenzo Librandi, Nov 22 2011

Maple

A022522:=n->(n + 1)^6 - n^6; seq(A022522(n), n=0..30); # Wesley Ivan Hurt, Jan 30 2014

Mathematica

Table[(n+1)^6-n^6, {n,0,30}] (* Vincenzo Librandi, Nov 22 2011 *)

PARI

a(n)=(n+1)^6-n^6 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[(n+1)^6 -n^6 for n in (0..30)] # G. C. Greubel, Aug 28 2019

Formula

G.f.: (1+x)*(1+56*x+246*x^2+56*x^3+x^4)/(1-x)^6. - Colin Barker, Dec 21 2012

a(n) = A005408(n) * A243201(n). - Mathew Englander, Jun 06 2014

a(n) = A001014(n+1) - A001014(n). - Wesley Ivan Hurt, Jun 06 2014

E.g.f.: (1 +62*x +270*x^2 +260*x^3 +75*x^4 +6*x^5)*exp(x). - G. C. Greubel, Aug 28 2019

G.f.: polylog(-6, 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

Extensions

More terms from Colin Barker, Dec 21 2012