cp's OEIS Frontend

A194449 Largest part minus the number of parts > 1 in the n-th region of the set of partitions of j, if 1 <= n <= A000041(j).

%I A194449 #29 Mar 11 2014 01:34:19
%S A194449 1,1,2,1,2,2,3,1,2,2,2,2,3,3,3,1,2,2,2,4,3,1,2,3,3,3,2,4,4,1,1,2,2,2,
%T A194449 4,3,1,3,5,5,4,-2,2,3,3,3,2,4,4,1,4,3,5,6,5,-3,1,2,2,2,4,3,1,3,5,5,4,
%U A194449 -2,2,4,4,5,3,6,6,5,-9
%N A194449 Largest part minus the number of parts > 1 in the n-th region of the set of partitions of j, if 1 <= n <= A000041(j).
%C A194449 Also triangle read by rows: T(j,k) = largest part minus the numbers of parts > 1 in the k-th region of the last section of the set of partitions of j. It appears that the sum of row j is equal to A000041(j-1). For the definition of "region" of the set of partitions of j see A206437. See also A135010.
%H A194449 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F A194449 a(n) = A141285(n) - A194448(n).
%e A194449 The 7th region of the shell model of partitions is [5, 2, 1, 1, 1, 1, 1]. The largest part is 5 and the number of parts > 1 is 2, so a(7) = 5 - 2 = 3 (see an illustration in the link section).
%e A194449 Written as an irregular triangle T(j,k) begins:
%e A194449 1;
%e A194449 1;
%e A194449 2;
%e A194449 1,2;
%e A194449 2,3;
%e A194449 1,2,2,2;
%e A194449 2,3,3,3;
%e A194449 1,2,2,2,4,3,1;
%e A194449 2,3,3,3,2,4,4,1;
%e A194449 1,2,2,2,4,3,1,3,5,5,4,-2;
%e A194449 2,3,3,3,2,4,4,1,4,3,5,6,5,-3;
%e A194449 1,2,2,2,4,3,1,3,5,5,4,-2,2,4,4,5,3,6,6,5,-9;
%Y A194449 Row j has length A187219(j).
%Y A194449 Cf. A000041, A135010, A138121, A138137, A138879, A186114, A186412, A193870, A194436, A194437, A194438, A194439, A194446, A194447, A206437.
%K A194449 sign,tabf
%O A194449 1,3
%A A194449 _Omar E. Pol_, Dec 10 2011