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%I #32 Jul 17 2014 18:29:05
%S 2,4,6,3,9,4,12,3,6,4,17,4,7,5,22,3,6,4,10,6,5,30,4,7,5,11,4,8,6,39,3,
%T 6,4,10,6,5,15,5,9,7,6,52,4,7,5,11,4,8,6,17,6,5,11,8,7,67,3,6,4,10,6,
%U 5,15,5,9,7,6,22,4,8,6,13,5,10,8
%N Largest part plus the number of parts of the n-th region of the section model of partitions.
%C Also semiperimeter of the n-th region of the geometric version of the section model of partitions. Note that a(n) is easily viewable as the sum of two perpendicular segments with a shared vertex. The horizontal segment has length A141285(n) and the vertical segment has length A194446(n). The difference between these two segments gives A194447(n). See also an illustration in the Links section. For the definition of "region" see A206437.
%C Also triangle read by rows: T(n,k) = largest part plus the number of parts of the k-th region of the last section of the set of partitions of n.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F a(n) = A141285(n) + A194446(n).
%e Written as a triangle begins:
%e 2;
%e 4;
%e 6;
%e 3, 9;
%e 4, 12;
%e 3, 6, 4, 17;
%e 4, 7, 5, 22;
%e 3, 6, 4, 10, 6, 5, 30;
%e 4, 7, 5, 11, 4, 8, 6, 39;
%e 3, 6, 4, 10, 6, 5, 15, 5, 9, 7, 6, 52;
%Y Row n has length A187219(n). Last term of row n is A133041(n). Where record occur give A000041, n >= 1.
%Y Cf. A002865, A135010, A182699, A182709, A183152, A194436, A194437, A194438, A194439, A194447, A206437.
%K nonn,tabf
%O 1,1
%A _Omar E. Pol_, Mar 08 2012
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