cp's OEIS Frontend

A230440 Triangle read by rows in which row n lists A000041(n-1) 1's followed by the list of partitions of n that do not contain 1 as a part in colexicographic order.

%I A230440 #24 Oct 26 2013 14:56:29
%S A230440 1,1,2,1,1,3,1,1,1,2,2,4,1,1,1,1,1,3,2,5,1,1,1,1,1,1,1,2,2,2,4,2,3,3,
%T A230440 6,1,1,1,1,1,1,1,1,1,1,1,3,2,2,5,2,4,3,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A230440 1,2,2,2,2,4,2,2,3,3,2,6,2,5,3,4,4,8
%N A230440 Triangle read by rows in which row n lists A000041(n-1) 1's followed by the list of partitions of n that do not contain 1 as a part in colexicographic order.
%C A230440 The n-th row of triangle lists the parts of the n-th section of the set of partitions of any integer >= n. For the definition of "section" see A135010.
%e A230440 Illustration of initial terms (row = 1..6). The table shows the six sections of the set of partitions of 6 in three ways. Note that before the dissection, the set of partitions was in colexicographic order, see A211992. More generally, in a master model, the six sections of the set of partitions of 6 also can be interpreted as the first six sections of the set of partitions of any integer >= 6.
%e A230440 ---------------------------------------------------------
%e A230440 n  j     Diagram          Parts              Parts
%e A230440 ---------------------------------------------------------
%e A230440 .         _
%e A230440 1  1     |_|              1;                 1;
%e A230440 .           _
%e A230440 2  1      _| |              1,                 1,
%e A230440 2  2     |_ _|              2;               2;
%e A230440 .             _
%e A230440 3  1         | |              1,                 1,
%e A230440 3  2      _ _| |              1,               1,
%e A230440 3  3     |_ _ _|              3;             3;
%e A230440 .               _
%e A230440 4  1           | |              1,                 1,
%e A230440 4  2           | |              1,               1,
%e A230440 4  3      _ _ _| |              1,             1,
%e A230440 4  4     |_ _|   |            2,2,           2,2,
%e A230440 4  5     |_ _ _ _|              4;           4;
%e A230440 .                 _
%e A230440 5  1             | |              1,                 1,
%e A230440 5  2             | |              1,               1,
%e A230440 5  3             | |              1,             1,
%e A230440 5  4             | |              1,             1,
%e A230440 5  5      _ _ _ _| |              1,           1,
%e A230440 5  6     |_ _ _|   |            3,2,         3,2,
%e A230440 5  7     |_ _ _ _ _|              5;         5;
%e A230440 .                   _
%e A230440 6  1               | |              1,                 1,
%e A230440 6  2               | |              1,               1,
%e A230440 6  3               | |              1,             1,
%e A230440 6  4               | |              1,             1,
%e A230440 6  5               | |              1,           1,
%e A230440 6  6               | |              1,           1,
%e A230440 6  7      _ _ _ _ _| |              1,         1,
%e A230440 6  8     |_ _|   |   |          2,2,2,       2,2,2,
%e A230440 6  9     |_ _ _ _|   |            4,2,       4,2,
%e A230440 6  10    |_ _ _|     |            3,3,       3,3,
%e A230440 6  11    |_ _ _ _ _ _|              6;       6;
%e A230440 ...
%e A230440 Triangle begins:
%e A230440 [1];
%e A230440 [1],[2];
%e A230440 [1],[1],[3];
%e A230440 [1],[1],[1],[2,2],[4];
%e A230440 [1],[1],[1],[1],[1],[3,2],[5];
%e A230440 [1],[1],[1],[1],[1],[1],[1],[2,2,2],[4,2],[3,3],[6];
%e A230440 ...
%Y A230440 Positive terms of A228716.
%Y A230440 Row n has length A138137(n).
%Y A230440 Row sums give A138879.
%Y A230440 Right border gives A000027.
%Y A230440 Cf. A000041, A135010, A138121, A141285, A182703, A187219, A193870, A194446, A206437, A207031, A207034, A207383, A207379, A211009.
%K A230440 nonn,tabf
%O A230440 1,3
%A A230440 _Omar E. Pol_, Oct 18 2013