cp's OEIS Frontend

A211009 Triangle read by rows: T(n,k) = number of cells in the k-column of the n-th region of j in the list of colexicographically ordered partitions of j, if 1<=n<=A000041(j), 1<=k<=A141285(n).

%I A211009 #29 Mar 11 2014 01:34:20
%S A211009 1,1,2,1,1,3,1,1,1,1,2,5,1,1,1,1,1,1,2,7,1,1,1,1,2,2,1,1,1,1,1,1,2,4,
%T A211009 11,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,2,4,15,1,1,1,1,2,2,1,1,1,1,1,1,2,
%U A211009 4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,7,22
%N A211009 Triangle read by rows: T(n,k) = number of cells in the k-column of the n-th region of j in the list of colexicographically ordered partitions of j, if 1<=n<=A000041(j), 1<=k<=A141285(n).
%C A211009 Also the finite sequence a(1)..a(r), where a(r) is a record in the sequence, is also a finite triangle read by rows: T(n,k) = number of cells in the k-column of the n-th region of the integer whose number of partitions is equal to a(r).
%C A211009 T(n,k) is also 1 plus the number of holes between T(n,k) and the previous member in the column k of triangle.
%C A211009 T(n,k) is also the height of the column mentioned in the definition, in a three-dimensional model of the set of partitions of j, in which the regions appear rotated 90 degrees and where the pivots are the largest part of every region (see A141285). For the definition of "region" see A206437. - _Omar E. Pol_, Feb 06 2014
%H A211009 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%e A211009 The irregular triangle begins:
%e A211009 1;
%e A211009 1, 2;
%e A211009 1, 1, 3;
%e A211009 1, 1;
%e A211009 1, 1, 2, 5;
%e A211009 1, 1, 1;
%e A211009 1, 1, 1, 2, 7;
%e A211009 1, 1;
%e A211009 1, 1, 2, 2;
%e A211009 1, 1, 1;
%e A211009 1, 1, 1, 2, 4, 11;
%e A211009 1, 1, 1;
%e A211009 1, 1, 1, 2, 2;
%e A211009 1, 1, 1, 1;
%e A211009 1, 1, 1, 1, 2, 4, 15;
%e A211009 1, 1;
%e A211009 1, 1, 2, 2;
%e A211009 1, 1, 1;
%e A211009 1, 1, 1, 2, 4, 4;
%e A211009 1, 1, 1, 1, 1;
%e A211009 1, 1, 1, 1;
%e A211009 1, 1, 1, 1, 2, 3, 7, 22;
%e A211009 ...
%e A211009 From _Omar E. Pol_, Feb 06 2014: (Start)
%e A211009 Illustration of initial terms:
%e A211009 .    _
%e A211009 .   |_|
%e A211009 .    1
%e A211009 .      _
%e A211009 .    _|_|
%e A211009 .   |_ _|
%e A211009 .    1 2
%e A211009 .        _
%e A211009 .       |_|
%e A211009 .    _ _|_|
%e A211009 .   |_ _ _|
%e A211009 .    1 1 3
%e A211009 .    _ _
%e A211009 .   |_ _|
%e A211009 .    1 1
%e A211009 .          _
%e A211009 .         |_|
%e A211009 .         |_|
%e A211009 .        _|_|
%e A211009 .    _ _|_ _|
%e A211009 .   |_ _ _ _|
%e A211009 .    1 1 2 5
%e A211009 .
%e A211009 (End)
%Y A211009 Records give positive terms of A000041. Row n has length A141285(n). Row sums give A186412.
%Y A211009 Cf. A040051, A135010, A182244, A182703, A186114, A187219, A193870, A194446, A206437.
%K A211009 nonn,tabf
%O A211009 1,3
%A A211009 _Omar E. Pol_, Oct 21 2012
%E A211009 Better definition from _Omar E. Pol_, Feb 06 2014