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A027596
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Sequence satisfies T^2(a)=a, where T is defined below.
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4
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1, 2, 2, 4, 4, 7, 8, 12, 13, 18, 21, 29, 33, 43, 49, 63, 71, 91, 103, 128, 143, 176, 198, 241, 271, 324, 363, 431, 483, 569, 636, 743, 827, 960, 1068, 1236, 1371, 1573, 1742, 1992, 2203, 2506, 2769, 3135, 3454, 3895, 4290, 4824, 5300, 5935, 6511, 7272, 7967
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OFFSET
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1,2
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COMMENTS
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The partition transform in A007213 expands m=5k as 1/(1-x^m) = 1 + x^m + x^2m + ..., whereas the transform here expands it as 1 + x^m. Thus, if m appears as an argument to the transform, a difference will occur at n=2m due to a difference in coefficient at x^2m. The smallest such m in A007212 (and A027595) is 25, which explains why this sequences differs from A007213 from n=50 onward. - Sean A. Irvine, Nov 10 2019
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REFERENCES
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S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, 11/96.
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
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FORMULA
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Define T:a->b by: given a1 <= a2 <= ..., let b(n) = number of ways of partitioning n into parts from a1, a2, ... such that parts = 0 mod 5 do not occur more than once.
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CROSSREFS
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KEYWORD
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nonn,eigen
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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