Search: id:A032020
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%I A032020
%S A032020 1,1,1,3,3,5,11,13,19,27,57,65,101,133,193,351,435,617,851,1177,1555,
%T A032020 2751,3297,4757,6293,8761,11305,15603,24315,30461,41867,55741,74875,
%U A032020 98043,130809,168425,257405,315973,431065,558327,751491,958265,1277867
%N A032020 Number of compositions (ordered partitions) of n into distinct parts.
%C A032020 a(n)= the number of different ways to run up a staircase with n steps, 
               taking steps of distinct sizes where the order matters and there 
               is no other restriction on the number or the size of each step taken. 
               - Mohammad K. Azarian (azarian(AT)evansville.edu), May 21 2008
%D A032020 B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes 
               Mathematicae 49 (1995), pp. 86-97.
%D A032020 Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem 
               II, Missouri Journal of Mathematical Sciences, Vol. 16, No. 1, Winter 
               2004, pp. 12-17.
%H A032020 T. D. Noe, <a href="b032020.txt">Table of n, a(n) for n=0..1000</a>
%H A032020 C. G. Bower, <a href="transforms2.html">Transforms (2)</a>
%F A032020 "AGK" (ordered, elements, unlabeled) transform of 1, 1, 1, 1...
%F A032020 G.f.: Sum(k >= 0; k! x^((k^2+k)/2) / Prod(1<=j<=k; 1-x^j)) - David W. 
               Wilson (davidwwilson(AT)comcast.net) May 04 2000
%e A032020 a(6) = 11 because 6 = 5+1 = 4+2 = 3+2+1 = 3+1+2 = 2+4 = 2+3+1 = 2+1+3 
               = 1+5 = 1+3+2 = 1+2+3
%Y A032020 Cf. A003242, A032011.
%Y A032020 Sequence in context: A100886 A072337 A132751 this_sequence A084656 A073749 
               A146918
%Y A032020 Adjacent sequences: A032017 A032018 A032019 this_sequence A032021 A032022 
               A032023
%K A032020 nonn,easy,nice
%O A032020 0,4
%A A032020 Christian G. Bower (bowerc(AT)usa.net), Apr 01 1998

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