cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A008513 Number of points on surface of 6-dimensional cube.

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%I A008513 #26 Sep 08 2022 08:44:36
%S A008513 0,64,728,4032,14896,42560,102024,215488,413792,737856,1240120,
%T A008513 1985984,3055248,4543552,6563816,9247680,12746944,17235008,22908312,
%U A008513 29987776,38720240,49379904,62269768
%N A008513 Number of points on surface of 6-dimensional cube.
%H A008513 Vincenzo Librandi, <a href="/A008513/b008513.txt">Table of n, a(n) for n = 0..10000</a>
%H A008513 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A008513 G.f.: 8*x*(8 + 43*x + 78*x^2 + 43*x^3 + 8*x^4)/(x-1)^6. - _Colin Barker_, Jan 02 2012
%F A008513 a(n) = 12*n^5 + 40*n^3 + 12*n. - _Charles R Greathouse IV_, Jan 02 2012
%F A008513 E.g.f.: 4*x*(16 +75*x +85*x^2 +30*x^3 +3*x^4)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p A008513 seq((n+1)^6-(n-1)^6, n=0..30);
%t A008513 Table[(n+1)^6-(n-1)^6, {n,0,30}] (* _G. C. Greubel_, Nov 09 2019 *)
%o A008513 (Magma) [(n+1)^6-(n-1)^6: n in [0..30]]; // _Vincenzo Librandi_, Aug 27 2011
%o A008513 (PARI) a(n)=n++^6-(n-2)^6 \\ _Charles R Greathouse IV_, Jan 02 2012
%o A008513 (Sage) [(n+1)^6-(n-1)^6 for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o A008513 (GAP) List([0..30], n-> (n+1)^6-(n-1)^6); # _G. C. Greubel_, Nov 09 2019
%K A008513 nonn,easy
%O A008513 0,2
%A A008513 _N. J. A. Sloane_