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A210763 Tetrahedron T(j,n,k) in which the slice j is a finite triangle read by rows T(n,k) which lists the sums of the columns of the shell model of partitions with n shells.

%I A210763 #13 Jun 01 2012 19:31:32
%S A210763 1,1,1,2,1,1,2,1,1,3,1,1,2,2,2,3,1,1,2,5,1,1,2,2,2,3,2,2,3,5,1,1,1,2,
%T A210763 7,1,1,2,2,2,3,3,3,3,5,3,3,4,4,7,1,1,1,2,4,11,1,1,2,2,2,3,3,3,3,5,4,4,
%U A210763 5,4,7,3,3,3,5,6,11,1,1,1,1,2,4,15
%N A210763 Tetrahedron T(j,n,k) in which the slice j is a finite triangle read by rows T(n,k) which lists the sums of the columns of the shell model of partitions with n shells.
%e A210763 --------------------------------------------------------
%e A210763 Illustration of first five                      A210952
%e A210763 slices of the tetrahedron                       Row sum
%e A210763 --------------------------------------------------------
%e A210763 . 1,                                               1
%e A210763 .    1,                                            1
%e A210763 .    1, 2,                                         3
%e A210763 .          1,                                      1
%e A210763 .          1, 2,                                   3
%e A210763 .          1, 1, 3,                                5
%e A210763 .                   1,                             1
%e A210763 .                   1, 2,                          3
%e A210763 .                   2, 2, 3,                       7
%e A210763 .                   1, 1, 2, 5,                    9
%e A210763 .                               1,                 1
%e A210763 .                               1, 2,              3
%e A210763 .                               2, 2, 3,           7
%e A210763 .                               2, 2, 3, 5,       12
%e A210763 .                               1, 1, 1, 2, 7,    12
%e A210763 --------------------------------------------------------
%e A210763 . 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7,
%e A210763 Each column sum in the slice j is equal to A000041(j).
%e A210763 .
%e A210763 Also this sequence can be written as a triangle read by rows in which each row is a flattened triangle. The sequence begins:
%e A210763 1;
%e A210763 1,1,2;
%e A210763 1,1,2,1,1,3;
%e A210763 1,1,2,2,2,3,1,1,2,5;
%e A210763 1,1,2,2,2,3,2,2,3,5,1,1,1,2,7;
%e A210763 1,1,2,2,2,3,3,3,3,5,3,3,4,4,7,1,1,1,2,4,11;
%e A210763 1,1,2,2,2,3,3,3,3,5,4,4,5,4,7,3,3,3,5,6,11,1,1,1,1,2,4,15;
%e A210763 Row n has length A000217(n). Row sums give A066186. Right border gives A000041(n), n >= 1.
%Y A210763 Cf. A135010, A138121, A209655, A209918, A210952, A210960, A210961.
%K A210763 nonn,tabf
%O A210763 1,4
%A A210763 _Omar E. Pol_, Apr 24 2012