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 A182284 #14 Dec 01 2013 13:35:01 %S A182284 1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,3,2,2,1,1,1,1,1,1, %T A182284 1,1,1,1,1,1,3,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,3,3,2,2,2,1,1,1, %U A182284 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A182284 Triangle read by rows: T(n,k) = number of parts in the k-th zone of the last section of the set of partitions of n. %e A182284 Illustration of three arrangements of the last section of the set of partitions of 7 and the zone numbers: %e A182284 -------------------------------------------------------- %e A182284 Zone \ a) b) c) %e A182284 -------------------------------------------------------- %e A182284 15 (7) (7) (. . . . . . 7) %e A182284 14 (4+3) (4+3) (. . . 4 . . 3) %e A182284 13 (5+2) (5+2) (. . . . 5 . 2) %e A182284 12 (3+2+2) (3+2+2) (. . 3 . 2 . 2) %e A182284 11 (1) (1) (1) %e A182284 10 (1) (1) (1) %e A182284 9 (1) (1) (1) %e A182284 8 (1) (1) (1) %e A182284 7 (1) (1) (1) %e A182284 6 (1) (1) (1) %e A182284 5 (1) (1) (1) %e A182284 4 (1) (1) (1) %e A182284 3 (1) (1) (1) %e A182284 2 (1) (1) (1) %e A182284 1 (1) (1) (1) %e A182284 . %e A182284 For n = 7 and k = 12 we can see that in the 12th zone of the last section there are three parts: 3, 2, 2, therefore T(7,12) = 3. %e A182284 Written as a triangle begins: %e A182284 1; %e A182284 1,1; %e A182284 1,1,1; %e A182284 1,1,1,2,1; %e A182284 1,1,1,1,1,2,1; %e A182284 1,1,1,1,1,1,1,3,2,2,1; %e A182284 1,1,1,1,1,1,1,1,1,1,1,3,2,2,1; %e A182284 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,3,3,2,2,2,1; %Y A182284 Row n has length A000041(n). Row sums give A138137. %Y A182284 Cf. A135010, A138121, A193173, A182285. %K A182284 nonn,tabf %O A182284 1,10 %A A182284 _Omar E. Pol_, Apr 23 2012