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