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A022522
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Nexus numbers (n+1)^6 - n^6.
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23
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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
(list;
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history;
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OFFSET
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0,2
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
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LINKS
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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).
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FORMULA
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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
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MAPLE
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A022522:=n->(n + 1)^6 - n^6; seq(A022522(n), n=0..30); # Wesley Ivan Hurt, Jan 30 2014
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MATHEMATICA
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Table[(n+1)^6-n^6, {n, 0, 30}] (* Vincenzo Librandi, Nov 22 2011 *)
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PROG
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(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
(Sage) [(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
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CROSSREFS
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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: A340902 A181125 A228221 * A152731 A090028 A152725
Adjacent sequences: A022519 A022520 A022521 * A022523 A022524 A022525
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jun 14 1998
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EXTENSIONS
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More terms from Colin Barker, Dec 21 2012
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STATUS
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approved
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