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A210960 Tetrahedron T(j,n,k) in which the slice j is a finite triangle read by rows T(n,k) which list the number of parts in the columns of the shell model of partitions with n shells mentioned in A210970. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 3, 2, 1, 1, 1, 3, 3, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 1, 3, 4, 3, 2, 1, 1, 1, 3, 4, 3, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

LINKS

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

EXAMPLE

--------------------------------------------------------

Illustration of first five

slices of the tetrahedron                       Row sum

--------------------------------------------------------

. 1,                                               1

.    1,                                            1

.    1, 1,                                         2

.          1,                                      1

.          1, 1,                                   2

.          1, 1, 1,                                3

.                   1,                             1

.                   1, 1,                          2

.                   2, 1, 1,                       4

.                   1, 2, 1, 1,                    5

.                               1,                 1

.                               1, 1,              2

.                               2, 1, 1,           4

.                               2, 2, 1, 1,        6

.                               1, 2, 2, 1, 1,     7

--------------------------------------------------------

. 1, 2, 1, 3, 2, 1, 5, 4, 2, 1, 7, 6, 4, 2, 1,

.

It appears that column sums give A058399.

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

1;

1,1,1,

1,1,1,1,1,1;

1,1,1,2,1,1,1,2,1,1;

1,1,1,2,1,1,2,2,1,1,1,2,2,1,1;

1,1,1,2,1,1,3,2,1,1,3,3,2,1,1,1,3,3,2,1,1;

1,1,1,2,1,1,3,2,1,1,4,3,2,1,1,3,4,3,2,1,1,1,3,4,3,2,1,1;

In which row sums give A006128.

CROSSREFS

Cf. A058399, A135010, A138121, A182703, A209655, A209918, A210763, A210961.

Sequence in context: A154843 A062557 A276438 * A193509 A003649 A287170

Adjacent sequences:  A210957 A210958 A210959 * A210961 A210962 A210963

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 22 2012

STATUS

approved

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Last modified November 13 23:48 EST 2019. Contains 329106 sequences. (Running on oeis4.)