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A021003 a(n) = (n/2)*(n^4 + 1).

%I A021003 #42 Sep 02 2025 06:07:46
%S A021003 0,1,17,123,514,1565,3891,8407,16388,29529,50005,80531,124422,185653,
%T A021003 268919,379695,524296,709937,944793,1238059,1600010,2042061,2576827,
%U A021003 3218183,3981324,4882825,5940701,7174467,8605198,10255589,12150015,14314591,16777232,19567713
%N A021003 a(n) = (n/2)*(n^4 + 1).
%C A021003 Magic constant for n X n X n X n hypercube (magic hypercube may not exist).
%H A021003 Kelvin Voskuijl, <a href="/A021003/b021003.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..595 from Vincenzo Librandi)
%H A021003 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MagicConstant.html">Magic Constant</a>.
%H A021003 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MagicTesseract.html">Magic Tesseract</a>.
%H A021003 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A021003 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), a(0)=0, a(1)=1, a(2)=17, a(3)=123, a(4)=514, a(5)=1565. - _Harvey P. Dale_, Dec 18 2011
%F A021003 a(n) = -a(-n) for all n in Z. - _Michael Somos_, Jul 11 2017
%F A021003 From _Elmo R. Oliveira_, Aug 31 2025: (Start)
%F A021003 G.f.: x*(1 + 11*x + 36*x^2 + 11*x^3 + x^4)/(x-1)^6.
%F A021003 E.g.f.: x*(2 + 15*x + 25*x^2 + 10*x^3 + x^4)*exp(x)/2. (End)
%t A021003 Table[(n(n^4+1))/2,{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,1,17,123,514,1565},40] (* _Harvey P. Dale_, Dec 18 2011 *)
%o A021003 (Magma) [(n/2)*(n^4+1): n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011
%o A021003 (PARI) {a(n) = (n^5 + n) / 2}; /* _Michael Somos_, Jul 11 2017 */
%Y A021003 Cf. A000217, A006003, A027441.
%K A021003 nonn,easy,changed
%O A021003 0,3
%A A021003 Arlin Anderson (starship1(AT)gmail.com)