cp's OEIS Frontend

A207379 Triangle read by rows: T(n,k) = number of parts that are in the k-th column of the last section of the set of partitions of n.

%I A207379 #24 Dec 01 2013 13:36:34
%S A207379 1,1,1,1,1,1,2,2,1,1,2,2,2,1,1,4,4,3,2,1,1,4,4,4,3,2,1,1,7,7,6,5,3,2,
%T A207379 1,1,8,8,8,6,5,3,2,1,1,12,12,11,10,7,5,3,2,1,1,14,14,14,12,10,7,5,3,2,
%U A207379 1,1,21,21,20,18,14,11,7,5,3,2,1,1
%N A207379 Triangle read by rows: T(n,k) = number of parts that are in the k-th column of the last section of the set of partitions of n.
%C A207379 Note that for n >= 2 the tail of the last section of n starts at the second column and the second column contains only one part of size 1, thus both the first and the second columns contain the same number of parts. For more information see A135010 and A182703.
%e A207379 Illustration of initial terms. First six rows of triangle as numbers of parts in the columns from the last sections of the first six natural numbers:
%e A207379 .                                       6
%e A207379 .                                       3 3
%e A207379 .                                       4 2
%e A207379 .                                       2 2 2
%e A207379 .                           5             1
%e A207379 .                           3 2             1
%e A207379 .                 4           1             1
%e A207379 .                 2 2           1             1
%e A207379 .         3         1           1             1
%e A207379 .   2       1         1           1             1
%e A207379 1     1       1         1           1             1
%e A207379 ---------------------------------------------------
%e A207379 1,  1,1,  1,1,1,  2,2,1,1,  2,2,2,1,1,  4,4,3,2,1,1
%e A207379 ...
%e A207379 Triangle begins:
%e A207379 1;
%e A207379 1,   1;
%e A207379 1,   1,  1;
%e A207379 2,   2,  1,  1;
%e A207379 2,   2,  2,  1,  1;
%e A207379 4,   4,  3,  2,  1,  1;
%e A207379 4,   4,  4,  3,  2,  1,  1;
%e A207379 7,   7,  6,  5,  3,  2,  1,  1;
%e A207379 8,   8,  8,  6,  5,  3,  2,  1,  1;
%e A207379 12, 12, 11, 10,  7,  5,  3,  2,  1,  1;
%e A207379 14, 14, 14, 12, 10,  7,  5,  3,  2,  1,  1;
%e A207379 21, 21, 20, 18, 14, 11,  7,  5,  3,  2,  1,  1;
%Y A207379 Column 1 is A187219. Row sums give A138137. Reversed rows converge to A000041.
%Y A207379 Cf. A002865, A058399, A135010, A138135, A181187, A207031, A207380.
%K A207379 nonn,tabl
%O A207379 1,7
%A A207379 _Omar E. Pol_, Mar 10 2012