cp's OEIS Frontend

A210971 Triangle read by rows in which row n lists the region number of the parts of the k-th partition of n, with partitions reverse lexicographically ordered.

%I A210971 #13 Mar 11 2014 01:34:20
%S A210971 1,3,2,6,5,3,11,10,8,9,5,18,17,15,16,12,13,7,29,28,26,27,23,24,18,28,
%T A210971 20,21,11
%N A210971 Triangle read by rows in which row n lists the region number of the parts of the k-th partition of n, with partitions reverse lexicographically ordered.
%C A210971 Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.
%H A210971 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%e A210971 For n = 5 we have:
%e A210971 ------------------------------------------------------
%e A210971 .              Two arrangements             Sum of
%e A210971 k           of the partitions of 5        partition k
%e A210971 ------------------------------------------------------
%e A210971 7      [5]                          [5]        5
%e A210971 6      [3+2]                      [3+2]        5
%e A210971 5      [4+1]                    [4  +1]        5
%e A210971 4      [2+1+1]                [2+2  +1]        5
%e A210971 3      [3+1+1]              [3  +1  +1]        5
%e A210971 2      [2+1+1+1]          [2+1  +1  +1]        5
%e A210971 1      [1+1+1+1+1]      [1+1+1  +1  +1]        5
%e A210971 ------------------------------------------------------
%e A210971 .              Two arrangements
%e A210971 .           of the region numbers           Sum of
%e A210971 k           of the partitions of 5          zone k
%e A210971 ------------------------------------------------------
%e A210971 7      [7]                          [7]        7
%e A210971 6      [6,7]                      [6,7]       13
%e A210971 5      [5,7]                    [5,  7]       12
%e A210971 4      [4,5,7]                [4,5,  7]       16
%e A210971 3      [3,5,7]              [3,  5,  7]       15
%e A210971 2      [2,3,5,7]          [2,3,  5,  7]       17
%e A210971 1      [1,2,3,5,7]      [1,2,3,  5,  7]       18
%e A210971 ------------------------------------------------------
%e A210971 So row 5 of triangle gives: 18, 17, 15, 16, 12, 13, 7.
%e A210971 .
%e A210971 Triangle begins:
%e A210971 1;
%e A210971 3,2;
%e A210971 6,5,3;
%e A210971 11,10,8,9,5;
%e A210971 18,17,15,16,12,13,7;
%e A210971 29,28,26,27,23,24,18,28,20,21,11;
%Y A210971 Column 1 is A026905. Right border = row lengths = A000041, n>=1. Row sums give A210972.
%Y A210971 Cf. A135010, A138121, A182703, A194446, A206437, A210969.
%K A210971 nonn,tabf,more
%O A210971 1,2
%A A210971 _Omar E. Pol_, Jun 30 2012