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.

A008512 Number of points on the surface of 5-dimensional cube.

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%I A008512 #28 Sep 08 2022 08:44:35
%S A008512 2,32,242,992,2882,6752,13682,24992,42242,67232,102002,148832,210242,
%T A008512 288992,388082,510752,660482,840992,1056242,1310432,1608002,1953632,
%U A008512 2352242,2808992,3329282,3918752
%N A008512 Number of points on the surface of 5-dimensional cube.
%H A008512 Vincenzo Librandi, <a href="/A008512/b008512.txt">Table of n, a(n) for n = 0..10000</a>
%H A008512 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A008512 a(n) = (n+1)^5 - (n-1)^5.
%F A008512 G.f.: (2 + 22*x + 102*x^2 + 82*x^3 + 32*x^4)/(1 - 5*x + 10*x^2 - 10*x^3 + 5*x^4 - x^5). - _Colin Barker_, Jan 02 2012
%F A008512 E.g.f.: 2*(1 +15*x +45*x^2 +30*x^3 +5*x^4)*exp(x). - _G. C. Greubel_, Nov 09 2019
%F A008512 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, May 04 2021
%p A008512 seq((n+1)^5-(n-1)^5, n=0..30);
%t A008512 Table[10n^2*(n^2+2)+2,{n,0,30}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{2,32,242,992,2882},30] (* _Harvey P. Dale_, Jul 17 2014 *)
%o A008512 (Magma) [(n+1)^5-(n-1)^5: n in [0..30]]; // _Vincenzo Librandi_, Aug 27 2011
%o A008512 (PARI) vector(31, n, n^5-(n-2)^5) \\ _G. C. Greubel_, Nov 09 2019
%o A008512 (Sage) [2*(1 +10*n^2 +5*n^4) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o A008512 (GAP) List([0..30], n-> 2*(1 +10*n^2 +5*n^4)); # _G. C. Greubel_, Nov 09 2019
%K A008512 nonn,easy
%O A008512 0,1
%A A008512 _N. J. A. Sloane_