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 A210990 #24 May 24 2012 13:07:25 %S A210990 0,3,10,21,26,44,51,75,80,92,99,136,143,157,166,213,218,230,237,260, %T A210990 271,280,348,355,369,378,403,410,427,438,526,531,543,550,573,584,593, %U A210990 631,640,659,672,683,804,811,825,834,859,866,883,894,938,949,958 %N A210990 Total area of the shadows of the three views of the shell model of partitions with n regions. %C A210990 Each part is represented by a cuboid of sides 1 X 1 X k where k is the size of the part. For the definition of "regions of n" see A206437. %F A210990 a(n) = A182244(n) + A182727(n) + A182181(n), n >= 1. %F A210990 a(A000041(n)) = 2*A006128(n) + A066186(n). %e A210990 For n = 11 the three views of the shell model of partitions with 11 regions look like this: %e A210990 . %e A210990 . A182181(11) = 35 A182244(11) = 66 %e A210990 . %e A210990 . 6 * * * * * 6 %e A210990 . 3 3 P * * 3 * * 3 %e A210990 . 2 4 a * * * 4 * 2 %e A210990 . 2 2 2 r * 2 * 2 * 2 %e A210990 . 1 5 t * * * * 5 1 %e A210990 . 1 2 3 i * * 3 * 2 1 %e A210990 . 1 1 4 t * * * 4 1 1 %e A210990 . 1 1 2 2 i * 2 * 2 1 1 %e A210990 . 1 1 1 3 o * * 3 1 1 1 %e A210990 . 1 1 1 1 2 n * 2 1 1 1 1 %e A210990 . 1 1 1 1 1 1 s 1 1 1 1 1 1 %e A210990 . <------- Regions ------ ------------> N %e A210990 . L %e A210990 . a 1 %e A210990 . r * 2 %e A210990 . g * * 3 %e A210990 . e * 2 %e A210990 . s * * * 4 %e A210990 . t * * 3 %e A210990 . * * * * 5 %e A210990 . p * 2 %e A210990 . a * * * 4 %e A210990 . r * * 3 %e A210990 . t * * * * * 6 %e A210990 . s %e A210990 . A182727(11) = 35 %e A210990 . %e A210990 The areas of the shadows of the three views are A182244(11) = 66, A182181(11) = 35 and A182727(11) = 35, therefore the total area of the three shadows is 66+35+35 = 136, so a(11) = 136. %Y A210990 Other versions: A207380, A210970, A210979, A210980, A210991. %Y A210990 Cf. A135010, A138121, A141285, A194446, A182181, A182727, A186114, A206437. %K A210990 nonn %O A210990 0,2 %A A210990 _Omar E. Pol_, Apr 23 2012