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Search: id:A097080
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| A097080 |
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Array T(n,k) = number of partitions of n into distinct odd parts in which k is the greatest part, for k=1,2,...,n, n>=1. |
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+0
1
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| 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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First T(n,k) not 0 or 1 is T(17,9)=2, which counts 1+7+9 and 3+5+9. Row sums: A000700.
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FORMULA
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T(n, 1)=0 for all n; T(n, n)=1 for all odd n>1; and for n>=3, T(n, k)=0 if k is even, else T(n, k)=Sum{T(n-k, i): i=1, 2, ..., n-1} for k=2, 3, ..., n-1.
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EXAMPLE
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First 5 rows:
1
0 0
0 0 1
0 0 1 0
0 0 0 0 1
Row 40 with even-numbered terms deleted:
0 0 0 0 0 0 2 5 6 7 6 5 4 3 2 1 1 1 1;
e.g., final 2 counts these two partitions:
9+31 and 1+3+5+31.
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CROSSREFS
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Cf. A000700.
Sequence in context: A014359 A079998 A027356 this_sequence A011746 A123192 A089510
Adjacent sequences: A097077 A097078 A097079 this_sequence A097081 A097082 A097083
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 23 2004
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