Search: id:A000929
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%I A000929
%S A000929 1,1,1,2,2,2,3,4,4,5,6,6,7,8,9,11,12,13,15,16,17,20,22,23,26,28,29,
%T A000929 32,35,37,41,45,47,51,55,58,63,68,72,77,82,86,92,98,103,111,118,123,
%U A000929 131,139,145,154,164,171,180,190,198,208,219,229,241,253,264,278,291
%N A000929 Dimension of n-th degree part of Steenrod algebra.
%C A000929 Number of partitions of n into parts of the form 2^j-1, j=1,2,... (called 
               s-partitions). Example: a(7)=4 because we have [7], [3,3,1], [3,1,
               1,1,1] and [1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 06 2006
%D A000929 P. C. P. Bhatt, An interesting way to partition a number, Inform. Process. 
               Lett., 71, 1999, 141-148.
%D A000929 W. M. Y. Goh, P. Hitczenko and A. Shokoufandeh, s-partitions, Inform. 
               Process. Lett., 82, 2002, 327-329.
%D A000929 Steenrod, N. and Epstein, D., "Cohomology Operations," Princeton Univ. 
               Press, 1962.
%H A000929 R. Zumkeller, <a href="b000929.txt">Table of n, a(n) for n = 0..512</
               a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 
               18 2009]
%F A000929 n-th term is number of ways to write n as a sum a_1 + ... + a_k where 
               the a_i are positive integers and a_i >= 2 * a_{i-1}.
%F A000929 1/product( (1-x^(2^i-1)),i=0..infinity) (Simon Plouffe).
%F A000929 a(n) = p(n,1) with p(n,k) = if k<=n then p(n-k,k)+p(n,2*k+1) else 0^n. 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 18 
               2009]
%p A000929 The sequence is C(n,n) where C := proc(m,n) option remember; local k, 
               a; if m = 0 then if n = 0 then 1 else 0 fi; elif m > n then C(n,n); 
               else a := 0; for k from 0 to m do a := a + C(floor(k/2), n-k) od; 
               a; fi end;
%p A000929 g:=1/product(1-x^(2^k-1),k=1..10): gser:=series(g,x=0,70): seq(coeff(gser,
               x,n),n=0..64); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 
               2006
%Y A000929 Cf. A117145.
%Y A000929 A000225, A000041, A018819, A079559. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 18 2009]
%Y A000929 Sequence in context: A070547 A094838 A025768 this_sequence A029146 A029053 
               A053254
%Y A000929 Adjacent sequences: A000926 A000927 A000928 this_sequence A000930 A000931 
               A000932
%K A000929 nonn
%O A000929 0,4
%A A000929 Dan Christensen [ jdchrist(AT)math.mit.edu ]

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