2,1

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.

Eric Weisstein's World of Mathematics, "Antimagic Square."

a(n) = n*(n^2-1)/2 - 1

a[3] = 29 because the antimagic constant of an antimagic square of order 4 must be at least 29 (see comments)

Table[n*(n^2-1)/2 - 1, {n, 2, 50}]

Cf. A117561, A050257, A049475.

Sequence in context: A061238 A046500 A062123 this_sequence A024178 A009312 A092275

Adjacent sequences: A117557 A117558 A117559 this_sequence A117561 A117562 A117563

easy,nonn

Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 29 2006