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%I #66 Dec 30 2022 06:33:07
%S 1,1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297
%N Number of regions in the set of partitions of n that contain only one part.
%C It appears that this is 1 together with A000041. - _Omar E. Pol_, Nov 29 2011
%C For the definition of "region" see A206437. See also A186114 and A193870.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F It appears that a(n) = A000041(n-2), if n >= 2. - _Omar E. Pol_, Nov 29 2011
%F It appears that a(n) = A000041(n) - A027336(n), if n >= 2. - _Omar E. Pol_, Nov 30 2011
%e For n = 5 the seven regions of 5 in nondecreasing order are the sets of positive integers of the rows as shown below:
%e 1;
%e 1, 2;
%e 1, 1, 3;
%e 0, 0, 0, 2;
%e 1, 1, 1, 2, 4;
%e 0, 0, 0, 0, 0, 3;
%e 1, 1, 1, 1, 1, 2, 5;
%e ...
%e There are three regions that contain only one positive part, so a(5) = 3.
%e Note that in every column of the triangle the positive integers are also the parts of one of the partitions of 5.
%Y Column 1 of A194438.
%Y Cf. A000041, A002865, A027336, A135010, A138121, A186114, A186412, A193870, A194436, A194437, A194446, A194447, A206437.
%K nonn,more
%O 1,4
%A _Omar E. Pol_, Nov 28 2011
%E Definition clarified by _Omar E. Pol_, May 21 2021
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