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 A210991 #21 May 24 2012 13:07:10 %S A210991 0,3,9,18,21,35,39,58,61,67,71,99,103,110,115,152,155,161,165,175,181, %T A210991 186,238,242,249,254,265,269,277,283,352,355,361,365,375,381,386,401, %U A210991 406,415,422,428,522,526,533,538,549,553,561,567,584,590,595,606 %N A210991 Total area of the shadows of the three views of the shell model of partitions with n regions. %C A210991 It appears that if n is a partition number A000041 then the rotated structure with n regions shows each row as a partition of k such that A000041(k) = n (see example). %C A210991 For the definition of "regions of n" see A206437. %F A210991 a(n) = A182181(n) + A182727(n) + A210692(n). %F A210991 a(A000041(n)) = 2*A006128(n) + A026905(n). %e A210991 For n = 11 the three views of the shell model of partitions with 11 regions look like this: %e A210991 . %e A210991 . A182181(11) = 35 A210692(11) = 29 %e A210991 . %e A210991 . 1 1 %e A210991 . 1 1 %e A210991 . 1 1 %e A210991 . 1 1 %e A210991 . 1 1 1 1 %e A210991 . 1 1 1 1 %e A210991 . 1 1 1 1 1 1 %e A210991 . 2 1 1 1 1 2 %e A210991 . 2 1 1 1 1 1 1 2 %e A210991 . 3 2 2 2 1 1 1 1 2 2 3 %e A210991 . 6 3 4 2 5 3 4 2 3 2 1 1 2 3 4 5 6 %e A210991 . <------- Regions ------ ------------> N %e A210991 . L %e A210991 . a 1 %e A210991 . r * 2 %e A210991 . g * * 3 %e A210991 . e * 2 %e A210991 . s * * * 4 %e A210991 . t * * 3 %e A210991 . * * * * 5 %e A210991 . p * 2 %e A210991 . a * * * 4 %e A210991 . r * * 3 %e A210991 . t * * * * * 6 %e A210991 . s %e A210991 . %e A210991 . A182727(11) = 35 %e A210991 . %e A210991 The areas of the shadows of the three views are A182181(11) = 35, A182727(11) = 35 and A210692(11) = 29, therefore the total area of the three shadows is 35+35+29 = 99, so a(11) = 99. %e A210991 Since n = 11 is a partition number A000041 we can see that the rotated structure with 11 regions shows each row as a partition of 6 because A000041(6) = 11. See below: %e A210991 . %e A210991 . 6 %e A210991 . 3 3 %e A210991 . 4 2 %e A210991 . 2 2 2 %e A210991 . 5 1 %e A210991 . 3 2 1 %e A210991 . 4 1 1 %e A210991 . 2 2 1 1 %e A210991 . 3 1 1 1 %e A210991 . 2 1 1 1 1 %e A210991 . 1 1 1 1 1 1 %e A210991 . %Y A210991 Other versions: A207380, A210970, A210979, A210980, A210990. %Y A210991 Cf. A000041, A026905, A135010, A138121, A141285, A182703, A194446, A182181, A182727, A186114, A206437, A210692. %K A210991 nonn %O A210991 0,2 %A A210991 _Omar E. Pol_, Apr 30 2012