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.
%I A117560 #23 Aug 20 2025 10:46:05
%S A117560 2,11,29,59,104,167,251,359,494,659,857,1091,1364,1679,2039,2447,2906,
%T A117560 3419,3989,4619,5312,6071,6899,7799,8774,9827,10961,12179,13484,14879,
%U A117560 16367,17951,19634,21419,23309,25307,27416,29639,31979,34439,37022,39731,42569
%N A117560 a(n) = n*(n^2 - 1)/2 - 1.
%C A117560 a(n-1) is an approximation for the lower bound of the "antimagic constant" of an antimagic square of order n. The antimagic constant here is defined as the least integer in the set of consecutive integers to which the rows, columns and diagonals of the square sum. By analogy with the magic constant. This approximation follows from the observation that (2*Sum_{k=1..n^2} k) + (m) + (m+1) <= Sum_{k=0..2*n+1} (m + k) where m is the antimagic constant for an antimagic square of order n. a(n) = A027480(n+1) - 1. Stricter bounds seem likely to exist. See A117561 for the upper bounds. Note there exist no antimagic squares of order two or three, but the values are indexed here for completeness.
%H A117560 Vincenzo Librandi, <a href="/A117560/b117560.txt">Table of n, a(n) for n = 2..5000</a>
%H A117560 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntimagicSquare.html">Antimagic Square</a>.
%H A117560 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A117560 a(n) = n*(n^2 - 1)/2 - 1.
%F A117560 G.f.: x^2*(2 + 3*x - 3*x^2 + x^3)/(1-x)^4. - _Colin Barker_, Mar 29 2012
%F A117560 From _Elmo R. Oliveira_, Aug 19 2025: (Start)
%F A117560 E.g.f.: 1 + x + (1 + x)*(-2 + 2*x + x^2)*exp(x)/2.
%F A117560 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 6. (End)
%e A117560 a(3) = 29 because the antimagic constant of an antimagic square of order 4 must be at least 29 (see comments).
%t A117560 Table[n*(n^2-1)/2 - 1, {n, 2, 50}]
%o A117560 (Magma) [n*(n^2-1)/2 - 1: n in [2..50]]; // _Vincenzo Librandi_, Jun 20 2011
%Y A117560 Cf. A027480, A049475, A050257, A117561.
%K A117560 easy,nonn
%O A117560 2,1
%A A117560 Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 29 2006