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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. 2
 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, 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, 5, 4, 7, 3, 3, 3, 5, 6, 11, 1, 1, 1, 1, 2, 4, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS EXAMPLE -------------------------------------------------------- Illustration of first five                      A210952 slices of the tetrahedron                       Row sum -------------------------------------------------------- . 1,                                               1 .    1,                                            1 .    1, 2,                                         3 .          1,                                      1 .          1, 2,                                   3 .          1, 1, 3,                                5 .                   1,                             1 .                   1, 2,                          3 .                   2, 2, 3,                       7 .                   1, 1, 2, 5,                    9 .                               1,                 1 .                               1, 2,              3 .                               2, 2, 3,           7 .                               2, 2, 3, 5,       12 .                               1, 1, 1, 2, 7,    12 -------------------------------------------------------- . 1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, Each column sum in the slice j is equal to A000041(j). . Also this sequence can be written as a triangle read by rows in which each row is a flattened triangle. The sequence begins: 1; 1,1,2; 1,1,2,1,1,3; 1,1,2,2,2,3,1,1,2,5; 1,1,2,2,2,3,2,2,3,5,1,1,1,2,7; 1,1,2,2,2,3,3,3,3,5,3,3,4,4,7,1,1,1,2,4,11; 1,1,2,2,2,3,3,3,3,5,4,4,5,4,7,3,3,3,5,6,11,1,1,1,1,2,4,15; Row n has length A000217(n). Row sums give A066186. Right border gives A000041(n), n >= 1. CROSSREFS Cf. A135010, A138121, A209655, A209918, A210952, A210960, A210961. Sequence in context: A213852 A051064 A153096 * A218799 A078770 A072038 Adjacent sequences:  A210760 A210761 A210762 * A210764 A210765 A210766 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Apr 24 2012 STATUS approved

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