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A210960
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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 list the number of parts in the columns of the shell model of partitions with n shells mentioned in A210970.
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2
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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
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OFFSET
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1,14
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LINKS
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EXAMPLE
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--------------------------------------------------------
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;
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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