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A194702
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Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (2 + m).
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9
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2, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1
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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 2. For further information see A182703 and A135010.
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LINKS
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Table of n, a(n) for n=1..91.
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FORMULA
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T(k,m) = A182703(2+m,k), with T(k,m) = 0 if k > 2+m.
T(k,m) = A194812(2+m,k).
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EXAMPLE
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Triangle begins:
2,
0, 2,
1, 0, 1,
0, 1, 0, 1,
0, 0, 1, 0, 1,
0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
...
For k = 1 and m = 1; T(1,1) = 2 because there are two parts of size 1 in the last section of the set of partitions of 3, since 2 + m = 3, so a(1) = 2. For k = 2 and m = 1; T(2,1) = 0 because there are no parts of size 2 in the last section of the set of partitions of 3, since 2 + m = 3, so a(2) = 0.
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CROSSREFS
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Always the sum of row k = p(2) = A000041(n) = 2.
The first (0-10) members of this family of triangles are A023531, A129186, this sequence, A194703-A194710.
Cf. A135010, A138121, A182712-A182714, A194812.
Sequence in context: A072627 A277144 A069848 * A118682 A198393 A083054
Adjacent sequences: A194699 A194700 A194701 * A194703 A194704 A194705
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KEYWORD
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nonn,tabl
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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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