%I A006894 M1254
%S A006894 1,2,4,11,67,2279,2598061,3374961778892,5695183504492614029263279,
%T A006894 16217557574922386301420536972254869595782763547561,
%U A006894 131504586847961235687181874578063117114329409897615188504091716162522225834932122128288032336298142
%N A006894 Number of planted 3-trees of height < n.
%C A006894 Representation requires n triangular numbers with greedy algorithm.
%C A006894 Comment from Marc LeBrun (mlb(AT)well.com): Maximum possible number of 
               distinct values after applying a commuting operation from 0 to N 
               times to a single initial value.
%C A006894 Divide the natural numbers in sets of consecutive numbers, starting with 
               {1}, each set with number of elements equal to the sum of elements 
               of the preceding set. The greatest element of the n-th set gives 
               a(n). The sets begin {1}, {2}, {3,4}, {5,6,7,8,9,10,11}, ... - Floor 
               van Lamoen (fvlamoen(AT)hotmail.com), Jan 16 2002
%C A006894 a(n+1) = (a(n)) th triangular numbers + 1 = A000217(a(n)) + 1. a(n) = 
               A072638(n-1) + 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Sep 11 2009]
%D A006894 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006894 F. Harary et al., Counting free binary trees..., J. Combin. Inform. System 
               Sciences, 17 (1992), 175-181.
%D A006894 E. Lemoine, ``Note sur deux nouvelles d\'{e}compositions des nombres 
               entiers,'' Assoc. fran\c{c}aise pour l'avancement des sciences. Vol. 
               29, pp. 72-74, 1900.
%H A006894 David Wasserman, <a href="b006894.txt">Table of n, a(n) for n = 1..14</
               a>
%H A006894 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%H A006894 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A006894 Partial sums of A002658; a(n+1) = a(n)(a(n)+1)/2 + 1 (from Marc LeBrun).
%F A006894 Sequence arises from a self-recursive process: a[1]=1, a[n]=a[n-1]*(a[n-1]+1)/
               2+1. E.g. a(1)=1, a(2)=1*2/2+1=2, a(3)=2*3/2+1=4, a(4)=4*5/2+1=11, 
               a(5)=11*12/2+1=67... - Miklos Kristof (kristmikl(AT)freemail.hu), 
               Dec 11 2007
%p A006894 A006894 := proc(n) option remember; if n=1 then 1 else A006894(n-1)*(A006894(n-1)+1)/
               2+1 fi end; [ seq(A006894(i),i=1..11) ];
%p A006894 a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n-1]+2,2) od: 
               seq(a[n]+1, n=-1..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 08 2007
%p A006894 a[1]:=1:for n from 2 to 10 do a[n]:=a[n-1]*(a[n-1]+1)/2+1 od: seq(a[n],
               n=1..10); - Miklos Kristof (kristmikl(AT)freemail.hu), Dec 11 2007
%Y A006894 Row sums of A036602.
%Y A006894 Sequence in context: A091233 A156434 A007903 this_sequence A038093 A057284 
               A156463
%Y A006894 Adjacent sequences: A006891 A006892 A006893 this_sequence A006895 A006896 
               A006897
%K A006894 nonn,easy,core,nice
%O A006894 1,2
%A A006894 Jeffrey Shallit, N. J. A. Sloane (njas(AT)research.att.com).