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, 158503681

Offset

0,2

References

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

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), pages 205-206.

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).

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

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 *)

Prog

(Magma) [(n+1)^6-n^6: n in [0..30]]; // Vincenzo Librandi, Nov 22 2011
(PARI) a(n)=(n+1)^6-n^6 \\ Charles R Greathouse IV, Sep 24 2015
(SageMath) [(n+1)^6 -n^6 for n in (0..30)] # G. C. Greubel, Aug 28 2019
(GAP) List([0..30], n-> (n+1)^6 - n^6); # G. C. Greubel, Aug 28 2019

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.

Sequence in context: A381120 A181125 A228221 * A152731 A090028 A152725

Adjacent sequences: A022519 A022520 A022521 * A022523 A022524 A022525

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 14 1998

Extensions

More terms from Colin Barker, Dec 21 2012

Status

approved