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 A206441 #22 Mar 14 2015 11:42:49 %S A206441 1,2,2,1,3,1,3,1,2,1,4,1,2,1,4,1,2,1,3,1,1,5,1,2,1,3,1,2,1,5,1,2,1,3, %T A206441 1,1,4,1,2,1,1,6 %N A206441 Triangle read by rows. T(n,k) = number of distinct parts in the k-th region of the last section of the set of partitions of n. %C A206441 a(n) is also the number of distinct parts in the n-th region of the shell model of partitions (see A135010 and A206437). %e A206441 The first region in the last section of the set of partitions of 6 looks like this: %e A206441 . ** %e A206441 There is only one part, so T(6,1) = 1. %e A206441 The second region in the last section of the set of partitions of 6 looks like this: %e A206441 . **** %e A206441 . ** %e A206441 There are two distinct parts, so T(6,2) = 2. %e A206441 The third region in the last section of the set of partitions of 6 looks like this: %e A206441 . *** %e A206441 There is only one part, so T(6,3) = 1. %e A206441 The 4th region in the last section of the set of partitions of 6 looks like this: %e A206441 . ****** %e A206441 . *** %e A206441 . ** %e A206441 . ** %e A206441 . * %e A206441 . * %e A206441 . * %e A206441 . * %e A206441 . * %e A206441 . * %e A206441 . * %e A206441 There are four distinct parts, so T(6,4) = 4. %e A206441 Written as a triangle: %e A206441 1; %e A206441 2; %e A206441 2; %e A206441 1, 3; %e A206441 1, 3; %e A206441 1, 2, 1, 4; %e A206441 1, 2, 1, 4; %e A206441 1, 2, 1, 3, 1, 1, 5; %e A206441 1, 2, 1, 3, 1, 2, 1, 5; %e A206441 1, 2, 1, 3, 1, 1, 4, 1, 2, 1, 1, 6; %Y A206441 Row n has length A187219(n). %Y A206441 Cf. A135010, A138121, A141285, A186412, A193870, A194436, A194437, A194438, A194439, A194446, A194447. %K A206441 nonn,tabf,more %O A206441 1,2 %A A206441 _Omar E. Pol_, Feb 13 2012