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.

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

Offset

1,4

Links

Table of n, a(n) for n=1..84.

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: A343407 A359236 A320010 * A281681 A218799 A078770

Adjacent sequences: A210760 A210761 A210762 * A210764 A210765 A210766

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 24 2012

Status

approved