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Search: id:A027293
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| A027293 |
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Triangular array T given by rows: P(n,k) = number of partitions of n that contain k as a part. |
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11
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| 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 3, 2, 1, 1, 7, 5, 3, 2, 1, 1, 11, 7, 5, 3, 2, 1, 1, 15, 11, 7, 5, 3, 2, 1, 1, 22, 15, 11, 7, 5, 3, 2, 1, 1, 30, 22, 15, 11, 7, 5, 3, 2, 1, 1, 42, 30, 22, 15, 11, 7, 5, 3, 2, 1, 1, 56, 42, 30, 22, 15, 11, 7, 5, 3, 2, 1, 1, 77
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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A027293 * an infinite lower triangular matrix with A010815 (1, -1, -1, 0, 0, 1,...) as the main diagonal the rest zeros = triangle A145975 having row sums = [1, 0, 0, 0,...]. These matrix operations are equivalent to the comment in A010815 stating "when convolved with the partition numbers = [1, 0, 0, 0,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 25 2008]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2008: (Start)
Row sums = A000070: (1, 2, 4, 7, 12, 19, 30, 45, 67,...)
A027293^2 = triangle A146023 (End)
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EXAMPLE
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Triangle begins:
1
1 1
2 1 1
3 2 1 1
5 3 2 1 1
7 5 3 2 1 1
11 7 5 3 2 1 1
15 11 7 5 3 2 1 1
22 15 11 7 5 3 2 1 1
30 22 15 11 7 5 3 2 1 1
42 30 22 15 11 7 5 3 2 1 1
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MATHEMATICA
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(* first *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{t = Flatten[Union /(AT) Partitions(AT)n]}, Table[Count[t, i], {i, n}]]; Array[f, 13] // Flatten.
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CROSSREFS
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Every column of T is A000041.
A145975, A010815 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 25 2008]
A000070, A146023 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2008]
Sequence in context: A093628 A114282 A112739 this_sequence A104762 A152462 A098805
Adjacent sequences: A027290 A027291 A027292 this_sequence A027294 A027295 A027296
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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)
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