Search: id:A040039
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%I A040039
%S A040039 1,1,2,2,3,3,5,5,7,7,10,10,13,13,18,18,23,23,30,30,37,37,
%T A040039 47,47,57,57,70,70,83,83,101,101,119,119,142,142,165,165,
%U A040039 195,195,225,225,262
%N A040039 First differences of A033485; also A033485 with terms repeated.
%C A040039 Comment from John MCKAY (mckay(AT)encs.concordia.ca), Mar 06 2009 (Start): 
               Apparently a(n) = number of partitions (p_1, p_2, ..., p_k) of n+1, 
               with p_1 >= p_2 >= ... >= p_k, such that for each i, p_i > p_{i+1}+...+p_k.
%p A040039 For example, the five partitions of 4, written in nonincreasing order, 
               are [1,1,1,1], [2,1,1], [2,2], [3,1], [4]. Only the last two satisfy 
               the condition, and a(3)=2. The Maple program below verifies this 
               for small values of n. (End)
%p A040039 (Maple code from John McKay) with(combinat); N:=8; a:=array(1..N); c:=array(1..N);
%p A040039 for n from 1 to N do p:=partition(n); np:=nops(p); t:=0;
%p A040039 for s to np do r:=p[s]; r:=sort(r,`>`); nr:=nops(r); j:=1;
%p A040039 while j<nr and r[j]>sum(r[k],k=j+1..nr) do j:=j+1;od; # gives A040039
%p A040039 #while j<nr and r[j]>= sum(r[k],k=j+1..nr) do j:=j+1;od; # gives A018819
%p A040039 if j=nr then t:=t+1;fi od; a[n]:=t; od;
%Y A040039 Cf. A000123, A018819.
%Y A040039 Cf. A018819, A088567, A089054.
%Y A040039 Sequence in context: A085885 A064986 A029019 this_sequence A008667 A109763 
               A119620
%Y A040039 Adjacent sequences: A040036 A040037 A040038 this_sequence A040040 A040041 
               A040042
%K A040039 nonn,easy,more
%O A040039 0,3
%A A040039 N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)

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