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 A117561 #14 Feb 16 2025 08:33:00
%S A117561 3,15,38,73,124,194,286,403,548,724,934,1181,1468,1798,2174,2599,3076,
%T A117561 3608,4198,4849,5564,6346,7198,8123,9124,10204,11366,12613,13948,
%U A117561 15374,16894,18511,20228,22048,23974,26009,28156,30418,32798,35299,37924
%N A117561 a(n) = floor(n*(n^3-n-3)/(2*(n-1))).
%C A117561 a[n-1] is one approximation for the upper 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 Sum[m + k, {k, 0, 2*n + 1}] <= (2*Sum[k, {k, 1, n^2}]) + (2*m) + (2*m + 1) where m is the antimagic constant for an antimagic square of order n. Stricter bounds seem likely to exist. See A117560 for the lower bounds. Note there exist no antimagic squares of order two or three, but the values are indexed here for completeness.
%H A117561 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntimagicSquare.html">Antimagic Square</a>.
%F A117561 a(n) = floor(n*(n^3-n-3)/(2*(n-1))).
%F A117561 G.f.: x^2*(3+3*x-4*x^2-x^3+3*x^4-x^5)/(1-x)^4. - _Colin Barker_, Mar 29 2012
%e A117561 a[3] = 38 because the antimagic constant of an antimagic square of order 4 cannot exceed 38 (see comments)
%t A117561 Table[Floor[n(n^3-n-3)/(2*(n-1))], {n, 2, 50}]
%Y A117561 Cf. A117560, A050257, A049475.
%K A117561 easy,nonn
%O A117561 2,1
%A A117561 Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 29 2006