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Search: id:A117561
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| A117561 |
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Floor[n*(n^3-n-3)/(2*(n-1))]. |
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+0
2
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| 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
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OFFSET
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2,1
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COMMENT
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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.
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LINKS
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Eric Weisstein's World of Mathematics, "Antimagic Square."
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FORMULA
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a(n) = Floor[n*(n^3-n-3)/(2*(n-1))]
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EXAMPLE
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a[3] = 38 because the antimagic constant of an antimagic square of order 4 cannot exceed 38 (see comments)
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MATHEMATICA
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Table[Floor[n(n^3-n-3)/(2*(n-1))], {n, 2, 50}]
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CROSSREFS
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Cf. A117560, A050257, A049475.
Sequence in context: A019009 A001803 A062741 this_sequence A065765 A014309 A096742
Adjacent sequences: A117558 A117559 A117560 this_sequence A117562 A117563 A117564
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KEYWORD
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easy,nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Mar 29 2006
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