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%I #25 Apr 11 2024 15:53:51
%S 4,6,8,12,16,24,32,46,62,86,114,156,204,272,354,464,596,772,982,1256,
%T 1586,2006,2512,3152,3918,4874,6022,7438,9132,11210,13686,16700,20288,
%U 24622,29768,35956,43276,52032,62372,74678,89168,106350
%N Number of segments needed to draw (on the infinite square grid) a diagram of regions and partitions of n.
%C On the infinite square grid the diagram of regions of the set of partitions of n is represented by a rectangle with base = n and height = A000041(n). The rectangle contains n shells. Each shell contains regions. Each row of a region is a part. Each part of size k contains k cells. The number of regions equals the number of partitions of n (see illustrations in the links section). For a minimalist version see A139582. For the definition of "region of n" see A206437.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa405.jpg">Illustration of initial terms of A211026 and of A066186</a>
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F a(n) = 2*A000041(n) + 2 = 2*A052810(n) = A139582(n) + 2.
%Y Cf. A000041, A052810, A135010, A139582, A141285, A186412, A186114, A187219, A193870, A194446, A194447, A206437, A211009
%K nonn,changed
%O 1,1
%A _Omar E. Pol_, Oct 29 2012
%E a(18) corrected by _Georg Fischer_, Apr 11 2024
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