Search: id:A117560
Results 1-1 of 1 results found.

%I A117560
%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
%N A117560 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, {k, 1, n^2}]) + (m) + (m+1) <= Sum[m + k, {k, 0, 2*n 
               + 1}] 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AntimagicSquare.html">"Antimagic Square."</a>
%F A117560 a(n) = n*(n^2-1)/2 - 1
%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}]
%Y A117560 Cf. A117561, A050257, A049475.
%Y A117560 Sequence in context: A061238 A046500 A062123 this_sequence A024178 A009312 
               A154251
%Y A117560 Adjacent sequences: A117557 A117558 A117559 this_sequence A117561 A117562 
               A117563
%K A117560 easy,nonn
%O A117560 2,1
%A A117560 Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 29 2006

Search completed in 0.001 seconds