cp's OEIS Frontend

A027482 a(n) = n*(n^3 - 1)/2.

%I A027482 #39 Oct 21 2022 21:10:33
%S A027482 7,39,126,310,645,1197,2044,3276,4995,7315,10362,14274,19201,25305,
%T A027482 32760,41752,52479,65151,79990,97230,117117,139909,165876,195300,
%U A027482 228475,265707,307314,353626,404985,461745,524272,592944,668151
%N A027482 a(n) = n*(n^3 - 1)/2.
%C A027482 Row sums in an n X n X n pandiagonal magic cube with entries (0..n^3-1).
%H A027482 Vincenzo Librandi, <a href="/A027482/b027482.txt">Table of n, a(n) for n = 2..1000</a>
%H A027482 S. Gartenhaus, <a href="https://arxiv.org/abs/math/0210275">Odd order pandiagonal latin and magic cubes in three and four dimensions</a>, arXiv:math/0210275 [math.CO], 2002.
%H A027482 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A027482 a(n) = A027478(n,n-1)
%F A027482 a(n) = A000217(n^2) - A000217(n). - _Jon Perry_, Jul 21 2003
%F A027482 a(n) = A058895(n)/2. - _Zerinvary Lajos_, Jan 28 2008
%F A027482 G.f.: x^2*(7 + 4*x + x^2)/(1 - x)^5. - _Vincenzo Librandi_, Dec 29 2012
%F A027482 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 6. - _Chai Wah Wu_, Apr 08 2021
%t A027482 Table[(m^4 - m)/2, {m, 44}] (* _Zerinvary Lajos_, Mar 21 2007 *)
%t A027482 CoefficientList[Series[(7 + 4*x + x^2)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 29 2012 *)
%o A027482 (PARI) t(n)=n*(n+1)/2;
%o A027482 for(n=0,50,print1(t(n^2)-t(n)","))
%o A027482 (Magma) [n * (n^3 - 1)/2: n in [2..50]]; // _Vincenzo Librandi_, Dec 29 2012
%Y A027482 First subdiagonal of A027478 (Cube of a triangular matrix constructed from the Stirling numbers of the first kind).
%K A027482 nonn,easy
%O A027482 2,1
%A A027482 _Olivier Gérard_