A027596 - OEIS

%I #9 Nov 11 2019 00:05:11

%S 1,2,2,4,4,7,8,12,13,18,21,29,33,43,49,63,71,91,103,128,143,176,198,

%T 241,271,324,363,431,483,569,636,743,827,960,1068,1236,1371,1573,1742,

%U 1992,2203,2506,2769,3135,3454,3895,4290,4824,5300,5935,6511,7272,7967

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

%C 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

%D S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, 11/96.

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%F 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.

%F A027596 = T(A027595). - _Sean A. Irvine_, Nov 10 2019

%Y Cf. A007213, A027595.

%K nonn,eigen

%O 1,2

%A _N. J. A. Sloane_, Dec 11 1999

%E Revised by _Sean A. Irvine_, Nov 10 2019