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 A210970 #22 May 23 2012 17:36:32 %S A210970 0,3,9,18,34,55,91,136,208,301,439,616,876,1203,1665,2256,3062,4083, %T A210970 5459,7186,9470,12335,16051,20688,26648,34027,43395,54966,69496,87341, %U A210970 109591,136766,170382,211293,261519,322382,396694,486327,595143,725954,883912 %N A210970 Total area of the shadows of the three views of a three-dimensional version of the shell model of partitions with n shells. %C A210970 For more information see A135010 and A182703. %F A210970 a(n) = 2*A006128(n) + A000217(n). %e A210970 For n = 6 the illustration of the three views of a three-dimensional version of the shell model of partitions with 6 shells looks like this: %e A210970 . %e A210970 . A006128(6) = 35 A006128(6) = 35 %e A210970 . %e A210970 . 6 6 %e A210970 . 3 3 3 3 %e A210970 . 4 2 4 2 %e A210970 . 2 2 2 2 2 2 %e A210970 . 5 1 5 1 %e A210970 . 3 2 1 3 2 1 %e A210970 . 4 1 1 4 1 1 %e A210970 . 2 2 1 1 2 2 1 1 %e A210970 . 3 1 1 1 3 1 1 1 %e A210970 . 2 1 1 1 1 2 1 1 1 1 %e A210970 . 1 1 1 1 1 1 1 1 1 1 1 1 %e A210970 . %e A210970 . %e A210970 . 1 2 5 9 12 6 \ %e A210970 . 1 1 3 5 6 \ %e A210970 . 1 1 2 4 \ 6th slice of %e A210970 . 1 1 2 / tetrahedron A210961 %e A210970 . 1 1 / %e A210970 . 1 / %e A210970 . %e A210970 . A000217(6) = 21 %e A210970 . %e A210970 The areas of the shadows of the three views are A006128(6) = 35, A006128(6) = 35 and A000217(6) = 21, therefore the total area of the three shadows is 35+35+21 = 91, so a(6) = 91. %Y A210970 Other versions: A207380, A210979, A210980, A210990, A210991. %Y A210970 Cf. A000217, A006128, A066186, A135010, A138121, A182703, A206437, A210952, A210961. %K A210970 nonn %O A210970 0,2 %A A210970 _Omar E. Pol_, Apr 22 2012