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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.

A182377 Total sum of positive ranks of all regions in the last shell of n.

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%I A182377 #15 Mar 11 2014 01:34:17
%S A182377 0,0,0,1,2,5,8,14,21,32,45,67,91
%N A182377 Total sum of positive ranks of all regions in the last shell of n.
%C A182377 The rank of a region of n is the largest part minus the number of parts. For the definition of "region of n" see A206437. For the definition of "last shell of n" see A135010.
%C A182377 a(n) is also the sum of positive integers in row n of triangle A194447. First differs from A000094 at a(12).
%H A182377 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%e A182377 For n = 7 the last shell of 7 contains four regions: [3],[5,2],[4],[7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] so we have:
%e A182377 ----------------------------------------------------------
%e A182377 .        Largest    Number
%e A182377 Region     part    of parts    Rank
%e A182377 ----------------------------------------------------------
%e A182377 .  1        3         1          2
%e A182377 .  2        5         2          3
%e A182377 .  3        4         1          3
%e A182377 .  4        7        15         -8
%e A182377 .
%e A182377 The sum of positive ranks is a(7) = 2 + 3 + 3 = 8.
%Y A182377 Cf. A000094, A135010, A138121, A182699, A182709, A183152, A186114, A187219, A194436-A194439, A194447-A194448, A196025,  A206437, A209616.
%K A182377 nonn,more
%O A182377 1,5
%A A182377 _Omar E. Pol_, Apr 29 2012