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.

A027484 a(n) = n*(n^4-1)/2.

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%I A027484 #27 Aug 02 2024 11:49:29
%S A027484 15,120,510,1560,3885,8400,16380,29520,49995,80520,124410,185640,
%T A027484 268905,379680,524280,709920,944775,1238040,1599990,2042040,2576805,
%U A027484 3218160,3981300,4882800,5940675,7174440,8605170,10255560,12149985
%N A027484 a(n) = n*(n^4-1)/2.
%C A027484 Row sums in a pandiagonal magic 4D-cube with entries (0..n^4-1).
%C A027484 Can be computed from the fourth power of a matrix constructed with the Stirling numbers of the first kind (see A027479).
%H A027484 Vincenzo Librandi, <a href="/A027484/b027484.txt">Table of n, a(n) for n = 2..1000</a>
%H A027484 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 A027484 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A027484 From _Chai Wah Wu_, Apr 08 2021: (Start)
%F A027484 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) for n > 7.
%F A027484 G.f.: 15*x^2*(x + 1)^2/(x - 1)^6. (End)
%t A027484 Table[(m^5 - m)/2, {m, 34}] (* _Zerinvary Lajos_, Mar 21 2007 *)
%t A027484 LinearRecurrence[{6,-15,20,-15,6,-1},{15,120,510,1560,3885,8400},30] (* _Harvey P. Dale_, Aug 02 2024 *)
%o A027484 (Magma) [n*(n^4 - 1)/2: n in [2..50]];// _Vincenzo Librandi_, Dec 29 2012
%o A027484 (PARI) a(n)=n*(n^4-1)/2 \\ _Charles R Greathouse IV_, Oct 21 2022
%Y A027484 First subdiagonal of A027479.
%K A027484 nonn,easy
%O A027484 2,1
%A A027484 _Olivier Gérard_