This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A027596 #9 Nov 11 2019 00:05:11 %S A027596 1,2,2,4,4,7,8,12,13,18,21,29,33,43,49,63,71,91,103,128,143,176,198, %T A027596 241,271,324,363,431,483,569,636,743,827,960,1068,1236,1371,1573,1742, %U A027596 1992,2203,2506,2769,3135,3454,3895,4290,4824,5300,5935,6511,7272,7967 %N A027596 Sequence satisfies T^2(a)=a, where T is defined below. %C A027596 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 A027596 S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, 11/96. %H A027596 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 A027596 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 A027596 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 A027596 = T(A027595). - _Sean A. Irvine_, Nov 10 2019 %Y A027596 Cf. A007213, A027595. %K A027596 nonn,eigen %O A027596 1,2 %A A027596 _N. J. A. Sloane_, Dec 11 1999 %E A027596 Revised by _Sean A. Irvine_, Nov 10 2019