A117561 a(n) = floor(n*(n^3-n-3)/(2*(n-1))).

3, 15, 38, 73, 124, 194, 286, 403, 548, 724, 934, 1181, 1468, 1798, 2174, 2599, 3076, 3608, 4198, 4849, 5564, 6346, 7198, 8123, 9124, 10204, 11366, 12613, 13948, 15374, 16894, 18511, 20228, 22048, 23974, 26009, 28156, 30418, 32798, 35299, 37924

Offset: 2

Author

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

Keywords

• easy
• nonn

Comments

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.

Examples

			a[3] = 38 because the antimagic constant of an antimagic square of order 4 cannot exceed 38 (see comments)
		

Links

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

Crossrefs

Cf. A117560, A050257, A049475.

Programs

Mathematica

Table[Floor[n(n^3-n-3)/(2*(n-1))], {n, 2, 50}]

Formula

a(n) = floor(n*(n^3-n-3)/(2*(n-1))).

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