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A194708
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Triangle read by rows: T(k,m) = number of occurrences of k in the outer shell of the partitions of (8 + m).
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2
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OFFSET
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1,1
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COMMENTS
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Sub-triangle of A182703 and also of A194812. Note that the sum of every row is also the number of partitions of 8. For further information see A182703 and A135010.
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LINKS
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Table of n, a(n) for n=1..10.
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FORMULA
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T(k,m) = A182703(8+m,k), with T(k,m) = 0 if k > 8+m.
T(k,m) = A194812(8+m,k).
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EXAMPLE
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Triangle begins:
22,
7, 15,
6, 6, 10,
2, 5, 5, 10,
2, 3, 4, 5, 8,
...
For k = 1 and m = 1; T(1,1) = 22 because there are 22 parts of size 1 in the outer shell of the partitions of 9, since 8 + m = 9, so a(1) = 22. For k = 2 and m = 1; T(2,1) = 7 because there are seven parts of size 2 in the outer shell of the partitions of 9, since 8 + m = 9, so a(2) = 7.
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CROSSREFS
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Always the sum of row k = p(8) = A000041(8) = 22.
The first (0-10) members of this family of triangles are A023531, A129186, A194702-A194707, this sequence, A194709, A194710.
Cf. A135010, A138121, A194812.
Sequence in context: A040469 A040468 A040467 * A069285 A159990 A040466
Adjacent sequences: A194705 A194706 A194707 * A194709 A194710 A194711
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KEYWORD
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nonn,tabl,more
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AUTHOR
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Omar E. Pol, Feb 05 2012
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STATUS
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approved
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