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 A209918 #36 Mar 13 2015 22:56:41 %S A209918 1,2,1,1,3,2,1,1,1,1,5,4,2,1,1,2,2,1,1,1,7,6,4,2,1,1,2,3,2,1,1,2,1,1,1 %N A209918 Tetrahedron in which the n-th slice is also one of the three views of the shell model of partitions of A207380 with n shells. %C A209918 Each slice of the tetrahedron is a triangle, thus the number of elements in the n-th slice is A000217(n). The slices are perpendicular to the slices of A026792. Each element of the n-th slice equals the volume of a column of the shell model of partitions with n shells. The sum of each column of the n-th slice is A000041(n). The sum of all elements of the n-th slice is A066186(n). %C A209918 It appears that the triangle formed by the first row of each slice gives A058399. %C A209918 It appears that the triangle formed by the last column of each slice gives A008284 and A058398. %C A209918 Also consider a vertical rectangle on the infinite square grid with shorter side = n and longer side = p(n) = A000041(n). Each row of rectangle represents a partition of n. Each part of each partition of n is a horizontal rectangle with shorter side = 1 and longer side = k, where k is the size of the part. It appears that T(n,k,j) is also the number of k-th parts of all partitions of n in the j-th column of rectangle. %e A209918 --------------------------------------------------------- %e A209918 Illustration of first five A181187 %e A209918 slices of the tetrahedron Row sum %e A209918 --------------------------------------------------------- %e A209918 . 1, 1 %e A209918 . 2, 1, 3 %e A209918 . 1, 1 %e A209918 . 3, 2, 1 6 %e A209918 . 1, 1, 2 %e A209918 . 1, 1 %e A209918 . 5, 4, 2, 1, 12 %e A209918 . 1, 2, 2, 5 %e A209918 . 1, 1 2 %e A209918 . 1, 1 %e A209918 . 7, 6, 4, 2, 1, 20 %e A209918 . 1, 2, 3, 2, 8 %e A209918 . 1, 1, 2, 4 %e A209918 . 1, 1, 2 %e A209918 . 1, 1 %e A209918 -------------------------------------------------------- %e A209918 . 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, %e A209918 . %e A209918 Note that the 5th slice appears as one of three views of the model in the example section of A207380. %Y A209918 Row sums give A181187. Column sums give A209656. Main diagonal gives A210765. Another version is A209655. %Y A209918 Cf. A000041, A000217, A002260, A004736, A008284, A026792, A058398, A058399, A066186, A135010, A182703, A182715, A207380. %K A209918 nonn,tabf,more %O A209918 1,2 %A A209918 _Omar E. Pol_, Mar 26 2012