A027596 Sequence satisfies T^2(a)=a, where T is defined below.

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

Table of n, a(n) for n=1..53.

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

Cf. A007213, A027595.

Sequence in context: A050366 A332753 A027591 * A007213 A097851 A266778

Adjacent sequences: A027593 A027594 A027595 * A027597 A027598 A027599

Keyword

nonn,eigen

Author

N. J. A. Sloane, Dec 11 1999

Extensions

Revised by Sean A. Irvine, Nov 10 2019

Status

approved