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.
%I A194439 #66 Dec 30 2022 06:33:07 %S A194439 1,1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297 %N A194439 Number of regions in the set of partitions of n that contain only one part. %C A194439 It appears that this is 1 together with A000041. - _Omar E. Pol_, Nov 29 2011 %C A194439 For the definition of "region" see A206437. See also A186114 and A193870. %H A194439 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a> %F A194439 It appears that a(n) = A000041(n-2), if n >= 2. - _Omar E. Pol_, Nov 29 2011 %F A194439 It appears that a(n) = A000041(n) - A027336(n), if n >= 2. - _Omar E. Pol_, Nov 30 2011 %e A194439 For n = 5 the seven regions of 5 in nondecreasing order are the sets of positive integers of the rows as shown below: %e A194439 1; %e A194439 1, 2; %e A194439 1, 1, 3; %e A194439 0, 0, 0, 2; %e A194439 1, 1, 1, 2, 4; %e A194439 0, 0, 0, 0, 0, 3; %e A194439 1, 1, 1, 1, 1, 2, 5; %e A194439 ... %e A194439 There are three regions that contain only one positive part, so a(5) = 3. %e A194439 Note that in every column of the triangle the positive integers are also the parts of one of the partitions of 5. %Y A194439 Column 1 of A194438. %Y A194439 Cf. A000041, A002865, A027336, A135010, A138121, A186114, A186412, A193870, A194436, A194437, A194446, A194447, A206437. %K A194439 nonn,more %O A194439 1,4 %A A194439 _Omar E. Pol_, Nov 28 2011 %E A194439 Definition clarified by _Omar E. Pol_, May 21 2021