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 A182285 #20 Dec 01 2013 13:35:01 %S A182285 1,1,2,1,1,3,1,1,1,4,4,1,1,1,1,1,5,5,1,1,1,1,1,1,1,6,6,6,6,1,1,1,1,1, %T A182285 1,1,1,1,1,1,7,7,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,8,8,8,8,1,1, %U A182285 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A182285 Triangle read by rows: T(n,k) = sum of all parts in the k-th zone of the last section of the set of partitions of n. %C A182285 Row n lists A000041(n-1) 1's together with A002865(n) n's. %e A182285 Illustration of three arrangements of the last section of the set of partitions of 7 and the zone numbers: %e A182285 -------------------------------------------------------- %e A182285 Zone \ a) b) c) %e A182285 -------------------------------------------------------- %e A182285 15 (7) (7) (. . . . . . 7) %e A182285 14 (4+3) (4+3) (. . . 4 . . 3) %e A182285 13 (5+2) (5+2) (. . . . 5 . 2) %e A182285 12 (3+2+2) (3+2+2) (. . 3 . 2 . 2) %e A182285 11 (1) (1) (1) %e A182285 10 (1) (1) (1) %e A182285 9 (1) (1) (1) %e A182285 8 (1) (1) (1) %e A182285 7 (1) (1) (1) %e A182285 6 (1) (1) (1) %e A182285 5 (1) (1) (1) %e A182285 4 (1) (1) (1) %e A182285 3 (1) (1) (1) %e A182285 2 (1) (1) (1) %e A182285 1 (1) (1) (1) %e A182285 . %e A182285 For n = 7 and k = 12 we can see that in the 12th zone of the last section of 7 the parts are 3, 2, 2, therefore T(7,12) = 3+2+2 = 7. %e A182285 Written as a triangle begins: %e A182285 1; %e A182285 1,2; %e A182285 1,1,3; %e A182285 1,1,1,4,4; %e A182285 1,1,1,1,1,5,5; %e A182285 1,1,1,1,1,1,1,6,6,6,6; %e A182285 1,1,1,1,1,1,1,1,1,1,1,7,7,7,7; %e A182285 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,8,8,8,8; %Y A182285 Row n has length A000041(n). Row sums give A138879. %Y A182285 Cf. A000041, A002865, A135010, A138121, A182284, A193173. %K A182285 nonn,tabf %O A182285 1,3 %A A182285 _Omar E. Pol_, Apr 23 2012