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A132011
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Number of partitions of n into distinct parts such that 3*u<=v for all pairs (u,v) of parts with u<v.
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3
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1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 40, 42, 43, 44, 47, 49, 50, 51, 54, 56, 57, 58, 61, 64, 66, 67, 70, 73, 75, 76, 79, 82, 84, 85, 88, 91
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Contribution from Edward Early (efedula(AT)alum.mit.edu), Jan 10 2009: (Start)
Also the dimension of the n-th degree part of the mod 3 Steenrod algebra.
Also the number of partitions into parts (3^j-1)/2=1+3+3^2+...+3^(j-1) for j>=1. (End)
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..1000
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FORMULA
| More generally, number of partitions of n into distinct parts such that m*u<=v for all pairs (u,v) of parts with u<v is equal to the number of partitions of n into parts of the form (m^k-1)/(m-1), thus g.f. for the number of such partitions is 1/Product_{k>0} (1-x^((m^k-1)/(m-1))). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Jan 09 2009]
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EXAMPLE
| a(10) = #{10, 9+1, 8+2} = 3;
a(11) = #{11, 10+1, 9+2} = 3;
a(12) = #{12, 11+1, 10+2, 9+3} = 4;
a(13) = #{13, 12+1, 11+2, 10+3, 9+3+1} = 5.
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CROSSREFS
| Cf. A000009, A000929.
A147583. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 08 2008]
Sequence in context: A194621 A088004 A070548 * A054893 A090617 A053693
Adjacent sequences: A132008 A132009 A132010 * A132012 A132013 A132014
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 07 2007
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