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A024162
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Number of incongruent integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 4, 7, 4, 8, 6, 10, 6, 11, 9, 14, 9, 16, 12, 18, 12, 21, 15, 24, 16, 25, 20, 30, 19, 33, 25, 33, 25, 40, 28, 44, 30, 44, 36, 52, 34, 55, 42, 56, 42, 65, 44, 70, 49, 67, 56, 78, 52, 85, 64, 83, 63, 96, 66, 102, 72, 95, 81, 113, 75, 120, 88, 115, 90
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OFFSET
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1,13
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REFERENCES
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A. M. Yaglom and I. M. Yaglom: Challenging Mathematical Problems with Elementary Solutions. Vol. I. Combinatorial Analysis and Probability Theory. New York: Dover Publications, Inc., 1987, p. 8, #30 (First published: San Francisco: Holden-Day, Inc., 1964)
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LINKS
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FORMULA
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For n=0..11 (mod 12), a(n) is respectively (n^2 + 6n - 7)/48, (n^2 - 4)/48, (n^2 + 6n + 21)/48, (n^2 - 16)/48, (n^2 + 6n - 7)/48, (n^2 + 12)/48, (n^2 + 6n + 5)/48, (n^2 - 16)/48, (n^2 + 6n + 9)/48, (n^2 - 4)/48, (n^2 + 6n + 5)/48
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CROSSREFS
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KEYWORD
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dead
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EXTENSIONS
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Apparently an erroneous version of A005044. For example a(18) should be 3 not 2.
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STATUS
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approved
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