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A008516 6-dimensional centered cube numbers.

%I A008516 #32 Sep 08 2022 08:44:36
%S A008516 1,65,793,4825,19721,62281,164305,379793,793585,1531441,2771561,
%T A008516 4757545,7812793,12356345,18920161,28167841,40914785,58149793,
%U A008516 81058105,111045881,149766121,199146025,261415793,339138865,435243601,553056401,696336265,869310793,1076713625,1323823321
%N A008516 6-dimensional centered cube numbers.
%C A008516 These are never prime, as a(n) = (2*n^2 + 2*n + 1) * (n^4 + 2*n^3 + 5*n^2 + 4*n + 1). - _Jonathan Vos Post_, Aug 17 2011
%H A008516 Vincenzo Librandi, <a href="/A008516/b008516.txt">Table of n, a(n) for n = 0..10000</a>
%H A008516 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A008516 From _Colin Barker_, Jul 09 2012: (Start)
%F A008516 G.f.: (1 + 58*x + 359*x^2 + 604*x^3 + 359*x^4 + 58*x^5 + x^6)/(1-x)^7.
%F A008516 a(n) = 1 + 6*n + 15*n^2 + 20*n^3 + 15*n^4 + 6*n^5 + 2*n^6. (End)
%F A008516 E.g.f.: (1 +64*x +332*x^2 +440*x^3 +205*x^4 +36*x^5 +2*x^6)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p A008516 seq(n^6+(n+1)^6, n=0..35);
%t A008516 Table[n^6 + (n+1)^6, {n,0,35}] (* _Alonso del Arte_, Aug 17 2011 *)
%t A008516 LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,65,793,4825,19721,62281,164305},30] (* _Harvey P. Dale_, Jun 19 2021 *)
%o A008516 (Magma) [(n+1)^6+n^6: n in [0..35]]; // _Vincenzo Librandi_, Aug 27 2011
%o A008516 (PARI) vector(36, n, n^6+(n-1)^6) \\ _G. C. Greubel_, Nov 09 2019
%o A008516 (Sage) [n^6+(n+1)^6 for n in (0..35)] # _G. C. Greubel_, Nov 09 2019
%o A008516 (GAP) List([0..35], n-> n^6+(n+1)^6); # _G. C. Greubel_, Nov 09 2019
%K A008516 nonn,easy
%O A008516 0,2
%A A008516 _N. J. A. Sloane_