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Search: id:A111802
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| A111802 |
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n^2-n-1 for n>3; a(1)=1; a(2)=2; a(3)=3. |
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+0
1
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| 1, 2, 3, 11, 19, 29, 41, 55, 71, 89, 109, 131, 155, 181, 209, 239, 271, 305, 341, 379, 419, 461, 505, 551, 599, 649, 701, 755, 811, 869, 929, 991, 1055, 1121, 1189, 1259, 1331, 1405, 1481, 1559, 1639, 1721, 1805, 1891, 1979, 2069, 2161, 2255, 2351, 2449, 2549
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Inspired by attempt to determine what incorrectly-named A000519 may really be. Conjecture: Sequence is number of different main-diagonal sums among Latin squares of order n. Confirmed for first five terms. Guaranteed to be an upper bound as the diagonal sum can only be in the range from n to n^2 inclusive and it is impossible for the sum to be n+1 or n^2-1. There is probably an easy proof that all other sums in this interval can be realized as the only restriction seems to be that it is not permissible for exactly n-1 numbers on a diagonal to be identical.
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FORMULA
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a(n) = n^2-n-1 = A028387(n-2) for n>3; a(n) = n for 1<=n<=3.
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EXAMPLE
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a(3) = 3, the number of different diagonal sums of all order 3 Latin squares. Their diagonal sums can only be 3, 6, and 9.
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CROSSREFS
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Cf. A028387 (n^2+3n+1).
Sequence in context: A025105 A095984 A135206 this_sequence A095282 A051071 A051095
Adjacent sequences: A111799 A111800 A111801 this_sequence A111803 A111804 A111805
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 17 2005
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