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A210763
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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.
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2
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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
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OFFSET
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1,4
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LINKS
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Table of n, a(n) for n=1..84.
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EXAMPLE
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--------------------------------------------------------
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).
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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.
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CROSSREFS
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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
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KEYWORD
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nonn,tabf
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AUTHOR
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Omar E. Pol, Apr 24 2012
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STATUS
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approved
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