cp's OEIS Frontend

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.

It is known that such matrices of size (2n+1) X (2n+1) do not exist.

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.