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A014591
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a(n) = floor(n^2/12 + 5/4).
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9
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1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 17, 20, 22, 25, 28, 31, 34, 38, 41, 45, 49, 53, 57, 62, 66, 71, 76, 81, 86, 92, 97, 103, 109, 115, 121, 128, 134, 141, 148, 155, 162, 170, 177, 185, 193, 201, 209, 218, 226, 235, 244, 253, 262, 272, 281, 291, 301, 311, 321
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OFFSET
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0,4
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COMMENTS
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Number of partitions of n + 10 into 4 distinct parts one of which is 3. - Michael Somos, Nov 03 2011
Number of partitions of n into 3 or fewer distinct parts. - Mo Li, Sep 27 2019
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LINKS
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FORMULA
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G.f.: (1/(1-x^3)-x^2)/(1-x)/(1-x^2).
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EXAMPLE
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1 + x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 6*x^8 + 8*x^9 + ...
10 = 4 + 3 + 2 + 1, 11 = 5 + 3 + 2 + 1, 12 = 6 + 3 + 2 + 1, 13 = 7 + 3 + 2 + 1 = 5 + 4 + 3 + 1, 14 = 8 + 3 + 2 + 1 = 5 + 4 + 3 + 2, 15 = 9 + 3 + 2 + 1 = 6 + 5 + 3 + 1 = 6 + 4 + 3 + 2.
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[k, 3], DuplicateFreeQ]], {k, 1, 50}] (* Mo Li, Sep 27 2019 *)
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PROG
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(PARI) {a(n) = (n^2 + 3) \ 12 + 1} /* Michael Somos, Nov 03 2011 */
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CROSSREFS
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It may be only a coincidence that the first 11 terms reproduce all available data on Vassiliev invariants from diagrams with u=2 univalent vertices, as recorded in the Kneissler paper.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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