A210945 - OEIS

A210945

Triangle read by rows: T(n,k) = number of parts in the k-th column of the mirror of the last shell of the partitions of n.

%I #27 May 21 2012 15:35:52

%S 1,2,3,5,1,7,1,11,3,1,15,3,1,22,6,3,1,30,7,4,1,42,11,7,3,1,56,13,9,4,

%T 1,77,20,15,8,3,1,101,23,18,10,4,1,135,33,27,17,8,3,1,176,40,34,22,11,

%U 4,1,231,54,47,33,18,8,3,1,297,65,58,42,24,11,4,1

%N Triangle read by rows: T(n,k) = number of parts in the k-th column of the mirror of the last shell of the partitions of n.

%C For another version see A207379.

%H Alois P. Heinz, <a href="/A210945/b210945.txt">Rows n = 1..70</a>

%e For n = 7 the illustration shows two arrangements of the last shell of the partitions of 7:

%e .

%e . (7) (7)

%e . (4+3) (3+4)

%e . (5+2) (2+5)

%e . (3+2+2) (2+2+3)

%e . (1) (1)

%e . --------

%e . 15,3,1

%e .

%e We can see that in the right hand picture (the mirror) the number of part for columns 1..3 are 15, 3, 1 therefore row 7 lists 15, 3, 1.

%e Written as a triangle begins:

%e 1;

%e 2;

%e 3;

%e 5, 1;

%e 7, 1;

%e 11, 3, 1;

%e 15, 3, 1;

%e 22, 6, 3, 1;

%e 30, 7, 4, 1;

%e 42, 11, 7, 3, 1;

%e 56, 13, 9, 4, 1;

%e 77, 20, 15, 8, 3, 1;

%e 101, 23, 18, 10, 4, 1;

%e 135, 33, 27, 17, 8, 3, 1;

%e 176, 40, 34, 22, 11, 4, 1;

%e 231, 54, 47, 33, 18, 8, 3, 1;

%e 297, 65, 58, 42, 24, 11, 4, 1;

%Y Column 1 is A000041,n >= 1. Column 2 is A083751. Column 3 is A119907. Row sums give A138137.

%Y Cf. A135010, A138121, A182717, A207379.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Apr 21 2012

%E More terms from _Alois P. Heinz_, May 07 2012