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 A194702 #29 Nov 30 2013 21:30:34 %S A194702 2,0,2,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1, %T A194702 0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0, %U A194702 0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1 %N A194702 Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (2 + m). %C A194702 Sub-triangle of A182703 and also of A194812. Note that the sum of every row is also the number of partitions of 2. For further information see A182703 and A135010. %F A194702 T(k,m) = A182703(2+m,k), with T(k,m) = 0 if k > 2+m. %F A194702 T(k,m) = A194812(2+m,k). %e A194702 Triangle begins: %e A194702 2, %e A194702 0, 2, %e A194702 1, 0, 1, %e A194702 0, 1, 0, 1, %e A194702 0, 0, 1, 0, 1, %e A194702 0, 0, 0, 1, 0, 1, %e A194702 0, 0, 0, 0, 1, 0, 1, %e A194702 0, 0, 0, 0, 0, 1, 0, 1, %e A194702 0, 0, 0, 0, 0, 0, 1, 0, 1, %e A194702 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, %e A194702 ... %e A194702 For k = 1 and m = 1; T(1,1) = 2 because there are two parts of size 1 in the last section of the set of partitions of 3, since 2 + m = 3, so a(1) = 2. For k = 2 and m = 1; T(2,1) = 0 because there are no parts of size 2 in the last section of the set of partitions of 3, since 2 + m = 3, so a(2) = 0. %Y A194702 Always the sum of row k = p(2) = A000041(n) = 2. %Y A194702 The first (0-10) members of this family of triangles are A023531, A129186, this sequence, A194703-A194710. %Y A194702 Cf. A135010, A138121, A182712-A182714, A194812. %K A194702 nonn,tabl %O A194702 1,1 %A A194702 _Omar E. Pol_, Feb 05 2012