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 A132011 Number of partitions of n into distinct parts such that 3*u<=v for all pairs (u,v) of parts with u
 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; text; internal format)
 OFFSET 1,4 COMMENTS From Edward Early, 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) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 FORMULA More generally, number of partitions of n into distinct parts such that m*u<=v for all pairs (u,v) of parts with u0} (1-x^((m^k-1)/(m-1))). - Vladeta Jovovic, Jan 09 2009 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. From Joerg Arndt, Dec 28 2012: (Start) The a(33)=17 such partitions of 33 are [ 1] [ 24 7 2 ] [ 2] [ 24 8 1 ] [ 3] [ 25 6 2 ] [ 4] [ 25 7 1 ] [ 5] [ 25 8 ] [ 6] [ 26 6 1 ] [ 7] [ 26 7 ] [ 8] [ 27 5 1 ] [ 9] [ 27 6 ] [10] [ 28 4 1 ] [11] [ 28 5 ] [12] [ 29 3 1 ] [13] [ 29 4 ] [14] [ 30 3 ] [15] [ 31 2 ] [16] [ 32 1 ] [17] [ 33 ] (End) PROG (Haskell) a132011 = p [1..] where p _ 0 = 1 p (k:ks) m = if m < k then 0 else p [3 * k ..] (m - k) + p ks m -- Reinhard Zumkeller, Oct 10 2013 CROSSREFS Cf. A000009, A000929. Cf. A147583. - Reinhard Zumkeller, Nov 08 2008 Sequence in context: A088004 A070548 A209628 * A363822 A054893 A090617 Adjacent sequences: A132008 A132009 A132010 * A132012 A132013 A132014 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 07 2007 STATUS approved

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Last modified August 9 10:37 EDT 2024. Contains 375040 sequences. (Running on oeis4.)