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A168604
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a(n) = 2^(n-2) - 1.
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12
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1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295, 8589934591
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OFFSET
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3,2
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COMMENTS
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Number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly two nonempty parts.
An elephant sequence, see A175655. For the central square six A[5] vectors, with decimal values between 26 and 176, lead to this sequence. For the corner squares these vectors lead to the companion sequence A000325 (without the first leading 1). - Johannes W. Meijer, Aug 15 2010
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LINKS
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FORMULA
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E.g.f.: 2*exp(2*x)-exp(x).
G.f.: x^3/((1-x)*(1-2*x))
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EXAMPLE
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The partitions of {1,1,1,2,3} into exactly two nonempty parts are {{1},{1,1,2,3}}, {{2},{1,1,1,3}}, {{3},{1,1,1,2}}, {{1,1},{1,2,3}}, {{1,2},{1,1,3}}, {{1,3},{1,1,2}} and {{2,3},{1,1,1}}.
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MATHEMATICA
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f4[n_] := 2^(n - 2) - 1; Table[f4[n], {n, 3, 30}]
LinearRecurrence[{3, -2}, {1, 3}, 40] (* Harvey P. Dale, Oct 20 2013 *)
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PROG
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CROSSREFS
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The number of ways of partitioning the multiset {1, 1, 1, 2, 3, ..., n-1} into exactly three and four nonempty parts are given in A168605 and A168606, respectively.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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