Search: id:A004250
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%I A004250 M1046
%S A004250 0,0,1,2,4,7,11,17,25,36,50,70,94,127,168,222,288,375,480,616,
%T A004250 781,990,1243,1562,1945,2422,2996,3703,4550,5588,6826,8332,
%U A004250 10126,12292,14865,17958,21618,25995,31165,37317,44562
%N A004250 Number of partitions of n into 3 or more parts.
%D A004250 N. Metropolis and P. R. Stein, The enumeration of graphical partitions, 
               Europ. J. Combin., 1 (1980), 139-1532.
%D A004250 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004250 P. R. Stein, On the number of graphical partitions, pp. 671-684 of Proc. 
               9th S-E Conf. Combinatorics, Graph Theory, Computing, Congr. Numer. 
               21 (1978).
%H A004250 T. M. Barnes and C. D. Savage, A recurrence for counting graphical partitions, 
               <a href="http://www.combinatorics.org/">Electronic J. Combinatorics</
               a>, 2 (1995)
%H A004250 <a href="Sindx_Gra.html#graph_part">Index entries for sequences related 
               to graphical partitions</a>
%H A004250 Eric Weisstein's World of Mathematics. <a href="http://mathworld.wolfram.com/
               Spider.html">Spider</a>
%H A004250 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Spider.html">Spider</a>
%F A004250 G.f.: sum(q^n / product( 1-q^k, k=1..n+3), n=0..inf) [ N. J. A. Sloane 
               (njas(AT)research.att.com) ].
%F A004250 a(n) = A000041(n)-floor((n+2)/2) = A058984(n)-1. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jun 18 2003
%F A004250 Let P(n,i) denote the number of partitions of n into i parts. Then a(n) 
               = sum_{i=3..n} P(n,i). - Thomas Wieder (thomas.wieder(AT)t-online.de), 
               Feb 01 2007
%e A004250 a(6)=7 because there are three partitions of n=6 with i=3 parts: [4, 
               1, 1], [3, 2, 1], [2, 2, 2] and two partitions with i=4 parts: [3, 
               1, 1, 1], [2, 2, 1, 1] and one partition with i=5 parts: [2, 1, 1, 
               1, 1]] and one partition with i=6 parts: [1, 1, 1, 1, 1, 1].
%p A004250 Maple program from Thomas Wieder (thomas.wieder(AT)t-online.de), Feb 
               01 2007: (Start)
%p A004250 with(combinat);
%p A004250 for i from 1 to 15 do pik(i,3) od;
%p A004250 pik:= proc(n::integer, k::integer)
%p A004250 # thomas.wieder(AT)t-online.de, 30.01.07
%p A004250 local i, Liste, Result;
%p A004250 if k > n or n < 0 or k < 1 then
%p A004250 return fail
%p A004250 end if;
%p A004250 Result := 0;
%p A004250 for i from k to n do
%p A004250 Liste:= PartitionList(n,i);
%p A004250 #print(Liste);
%p A004250 Result := Result + nops(Liste);
%p A004250 end do;
%p A004250 return Result;
%p A004250 end proc;
%p A004250 PartitionList := proc (n, k)
%p A004250 # Authors: Herbert S. Wilf and Joanna Nordlicht. Source: Lecture Notes 
               "East Side West Side,..." University of Pennsylvania, USA, 2002. 
               Avalible at: http://www.cis.upenn.edu/~wilf/lecnotes.html Calculates 
               the partition of n into k parts. E.g. PartitionList(5,2) --> [[4, 
               1], [3, 2]].
%p A004250 local East, West;
%p A004250 if n < 1 or k < 1 or n < k then
%p A004250 RETURN([])
%p A004250 elif n = 1 then
%p A004250 RETURN([[1]])
%p A004250 else if n < 2 or k < 2 or n < k then
%p A004250 West := []
%p A004250 else
%p A004250 West := map(proc (x) options operator, arrow;
%p A004250 [op(x), 1] end proc,PartitionList(n-1,k-1)) end if;
%p A004250 if k <= n-k then
%p A004250 East := map(proc (y) options operator, arrow;
%p A004250 map(proc (x) options operator, arrow; x+1 end proc,y) end proc,PartitionList(n-k,
               k))
%p A004250 else East := [] end if;
%p A004250 RETURN([op(West), op(East)])
%p A004250 end if;
%p A004250 end proc; # (End)
%p A004250 ZL :=[S, {S = Set(Cycle(Z),3 <= card)}, unlabelled]: seq(combstruct[count](ZL, 
               size=n), n=1..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 25 2008
%p A004250 B:=[S,{S = Set(Sequence(Z,1 <= card),card >=3)},unlabelled]: seq(combstruct[count](B, 
               size=n), n=1..41);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 21 2009]
%t A004250 Length /(AT) Table[Select[Partitions[n], Length[ # ] >= 3 &], {n, 20}] 
               - Eric Weisstein (eric(AT)weisstein.com), May 16 2007
%Y A004250 Cf. A000569, A004251, A029889, A035300, A095268.
%Y A004250 Sequence in context: A007000 A073472 A096914 this_sequence A084842 A096967 
               A117276
%Y A004250 Adjacent sequences: A004247 A004248 A004249 this_sequence A004251 A004252 
               A004253
%K A004250 nonn,easy
%O A004250 1,4
%A A004250 N. J. A. Sloane (njas(AT)research.att.com).
%E A004250 Definition corrected by Thomas Wieder (thomas.wieder(AT)t-online.de), 
               Feb 01 2007 and by Eric Weisstein (eric(AT)weisstein.com), May 16 
               2007

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