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Search: id:A117750
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| A117750 |
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A triangular form based on partitions A000041 in a Ramanujan congruence form : odd number form with reversed n and m. |
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+0
1
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| 30, 135, 490, 2436, 1575, 10143, 4565, 37338, 1300156, 792, 12310, 124754, 1575, 31185, 386155, 26543660, 75175, 1121505, 4835271870, 5604, 173525, 3087735, 10143, 386155, 8118264, 1327710076, 4328363658647, 25025873760111
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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From a marginal notation several years old in the book: I had a form for odd numbers and one for primes noted.
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REFERENCES
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Robert Kanigel, The Man Who Knew Infinity, Washington Square Press, New York,1991, page 302
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FORMULA
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a(n) = If[Mod[PartitionsP[(2*n + 1)*m + n + 2], 2*n + 1] == 0, PartitionsP[(2*n + 1)*m + n + 2], {}]
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EXAMPLE
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30, 135
490, 2436
1575, 10143
4565, 37338, 1300156
792, 12310, 124754
1575, 31185, 386155, 26543660
75175, 1121505, 4835271870
5604, 173525, 3087735
10143, 386155, 8118264, 1327710076, 4328363658647, 25025873760111
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MATHEMATICA
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b = Table[Flatten[Table[If[Mod[a[[( 2*n + 1)*m + n + 2]], 2*n + 1] == 0, PartitionsP[(2*n + 1)*m + n + 2], {}], {n, 1, m}]], {m, 1, 10}] Flatten[b]
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CROSSREFS
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Cf. A000041.
Adjacent sequences: A117747 A117748 A117749 this_sequence A117751 A117752 A117753
Sequence in context: A044743 A100147 A079588 this_sequence A158462 A064495 A124958
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2006
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