Search: id:A000094
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%I A000094 M1350 N0518
%S A000094 0,0,0,0,1,2,5,8,14,21,32,45,65,88,121,161,215,280,367,471,607,771,980,
%T A000094 1232,1551,1933,2410,2983,3690,4536,5574,6811,8317,10110,12276,14848,
%U A000094 17941,21600,25977,31146,37298,44542,53132,63218,75131,89089
%N A000094 Number of trees of diameter 4.
%C A000094 Number of partitions of n-1 with at least two parts of size 2 or larger. 
               - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
%C A000094 Also equal to the number of partitions p of n-1 such that max(p)-min(p) 
               > 1. Example: a(7)=5 because we have [5,1],[4,2],[4,1,1],[3,2,1] 
               and [3,1,1,1]. - Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 06 2006 
               END Also number of partitions of n-1 with at least two parts that 
               are smaller than the largest part. Example: a(7)=5 because we have 
               [4,1,1],[3,2,1],[3,1,1,1],[2,2,1,1,1] and [2,1,1,1,1]. - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), May 01 2006
%D A000094 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000094 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000094 J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. 
               Dev. 4 (1960), 473-478.
%H A000094 Christian G. Bower, <a href="b000094.txt">Table of n, a(n) for n=1..500</
               a>
%H A000094 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000094 G.f.=x/product(1-x^j,j=1..infinity)-x-x^2/(1-x)^2. G.f.=sum(sum(x^(i+j+1)/
               product(1-x^k, k=i..j), i=1..j-2), j=3..infinity). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), May 01 2006
%p A000094 g:=x/product(1-x^j,j=1..70)-x-x^2/(1-x)^2: gser:=series(g,x=0,48): seq(coeff(gser,
               x,n),n=1..46); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 
               2006
%Y A000094 a(n+1)=A000041(n)-n for n>0 - John W. Layman (layman(AT)math.vt.edu)
%Y A000094 Sequence in context: A006918 A165189 A011842 this_sequence A058578 A023674 
               A139218
%Y A000094 Adjacent sequences: A000091 A000092 A000093 this_sequence A000095 A000096 
               A000097
%K A000094 nonn
%O A000094 1,6
%A A000094 N. J. A. Sloane (njas(AT)research.att.com).
%E A000094 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 
               2006

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