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A027596
Sequence satisfies T^2(a)=a, where T is defined below.
4
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
OFFSET
1,2
COMMENTS
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
REFERENCES
S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, 11/96.
LINKS
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 arXiv version]
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]
FORMULA
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.
A027596 = T(A027595). - Sean A. Irvine, Nov 10 2019
CROSSREFS
Sequence in context: A050366 A332753 A027591 * A007213 A097851 A266778
KEYWORD
nonn,eigen
AUTHOR
N. J. A. Sloane, Dec 11 1999
EXTENSIONS
Revised by Sean A. Irvine, Nov 10 2019
STATUS
approved