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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 mentioned in A210970.
4

%I #15 May 23 2012 17:36:13

%S 1,1,2,1,1,2,1,3,1,1,1,2,1,5,1,1,4,3,1,1,1,2,1,5,1,1,7,3,1,1,5,3,2,1,

%T 1,1,2,1,5,1,1,9,3,1,1,12,5,2,1,1,6,6,4,2,1,1,1,2,1,5,1,1,9,3,1,1,15,

%U 5,2,1,1,15,8,4,2,1,1,7,6,5,3,2,1,1

%N 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 mentioned in A210970.

%e --------------------------------------------------------

%e Illustration of first five A210952

%e slices of the tetrahedron Row sum

%e --------------------------------------------------------

%e . 1, 1

%e . 1, 1

%e . 2, 1, 3

%e . 1, 1

%e . 2, 1, 3

%e . 3, 1, 1, 5

%e . 1, 1

%e . 2, 1, 3

%e . 5, 1, 1, 7

%e . 4, 3, 1, 1, 9

%e . 1, 1

%e . 2, 1, 3

%e . 5, 1, 1, 7

%e . 7, 3, 1, 1, 12

%e . 5, 3, 2, 1, 1, 12

%e --------------------------------------------------------

%e . 1, 3, 1, 6, 2, 1,12, 5, 2, 1,20, 8, 4, 2, 1,

%e .

%e Column sums give A181187.

%e Also, written as a triangle read by rows in which each row is a flattened triangle, begins:

%e 1;

%e 1,2,1;

%e 1,2,1,3,1,1;

%e 1,2,1,5,1,1,4,3,1,1;

%e 1,2,1,5,1,1,7,3,1,1,5,3,2,1,1;

%e 1,2,1,5,1,1,9,3,1,1,12,5,2,1,1,6,6,4,2,1,1;

%e 1,2,1,5,1,1,9,3,1,1,15,5,2,1,1,15,8,4,2,1,1,7,6,5,3,2,1,1;

%e In which row sums give A066186.

%Y Cf. A066186, A135010, A138121, A181187, A210952, A210960, A210970.

%K nonn,tabf

%O 1,3

%A _Omar E. Pol_, Apr 22 2012