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Search: id:A085472
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| A085472 |
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Number of partitions into distinct nonzero pairs (i,j) with i,j>=0, read by antidiagonals. Also number of partitions into such pairs that aren't divisible by 2. |
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1
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| 1, 1, 1, 1, 2, 1, 2, 3, 3, 2, 2, 5, 5, 5, 2, 3, 7, 9, 9, 7, 3, 4, 10, 14, 17, 14, 10, 4, 5, 14, 21, 27, 27, 21, 14, 5, 6, 19, 31, 42, 46, 42, 31, 19, 6, 8, 25, 44, 64, 74, 74, 64, 44, 25, 8, 10, 33, 61, 93, 116, 123, 116, 93, 61, 33, 10, 12, 43, 83, 132, 174, 197, 197, 174, 132, 83
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Partitions into distinct scalars (A000009) are the borders a(n,0)=a(0,n). Unrestricted partitions into (not necessarily distinct) pairs is A060243.
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FORMULA
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G.f.: 1/2 Product(1+x^i*y^j), i, j>=0.
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EXAMPLE
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a(17) = a(3,2) = 9 partitions into...
Distinct pairs: 32 31+01 30+02 22+10 21+11 21+10+01 20+12 20+11+01 20+10+02
Non-even pairs: 32 31+01 30+01+01 21+11 21+10+01 12+10+10 11+11+10 11+10+10+01 10+10+10+01+01
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CROSSREFS
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Cf. A000009, A060243.
Sequence in context: A165014 A058063 A143902 this_sequence A054242 A033767 A033775
Adjacent sequences: A085469 A085470 A085471 this_sequence A085473 A085474 A085475
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Jul 01 2003
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