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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 A210945 #27 May 21 2012 15:35:52
%S A210945 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 A210945 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 A210945 4,1,231,54,47,33,18,8,3,1,297,65,58,42,24,11,4,1
%N 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.
%C A210945 For another version see A207379.
%H A210945 Alois P. Heinz, <a href="/A210945/b210945.txt">Rows n = 1..70</a>
%e A210945 For n = 7 the illustration shows two arrangements of the last shell of the partitions of 7:
%e A210945 .
%e A210945 .       (7)        (7)
%e A210945 .     (4+3)        (3+4)
%e A210945 .     (5+2)        (2+5)
%e A210945 .   (3+2+2)        (2+2+3)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .       (1)        (1)
%e A210945 .                 --------
%e A210945 .                  15,3,1
%e A210945 .
%e A210945 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 A210945 Written as a triangle begins:
%e A210945 1;
%e A210945 2;
%e A210945 3;
%e A210945 5,    1;
%e A210945 7,    1;
%e A210945 11,   3,  1;
%e A210945 15,   3,  1;
%e A210945 22,   6,  3,  1;
%e A210945 30,   7,  4,  1;
%e A210945 42,  11,  7,  3,  1;
%e A210945 56,  13,  9,  4,  1;
%e A210945 77,  20, 15,  8,  3,  1;
%e A210945 101, 23, 18, 10,  4,  1;
%e A210945 135, 33, 27, 17,  8,  3,  1;
%e A210945 176, 40, 34, 22, 11,  4,  1;
%e A210945 231, 54, 47, 33, 18,  8,  3,  1;
%e A210945 297, 65, 58, 42, 24, 11,  4,  1;
%Y A210945 Column 1 is A000041,n >= 1. Column 2 is A083751. Column 3 is A119907. Row sums give A138137.
%Y A210945 Cf. A135010, A138121, A182717, A207379.
%K A210945 nonn,tabf
%O A210945 1,2
%A A210945 _Omar E. Pol_, Apr 21 2012
%E A210945 More terms from _Alois P. Heinz_, May 07 2012