%I A006893 M1533
%S A006893 1,2,5,20,230,26795,359026205,64449908476890320,
%T A006893 2076895351339769460477611370186680,
%U A006893 2156747150208372213435450937462082366919951682912789656986079991220
%N A006893 Smallest number whose representation requires n triangular numbers with 
               greedy algorithm; also number of 1-2 rooted trees of height n.
%D A006893 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006893 M. Abert and P. Diaconis, paper in preparation, 2002.
%D A006893 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.
%D A006893 D. Parisse, The Tower of Hanoi and the Stern-Brocot-Array, Thesis, Munich, 
               1997.
%H A006893 <a href="Sindx_St.html#Stern">Index entries for sequences related to 
               Stern's sequences</a>
%H A006893 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A006893 a(n+1) = a(n)*(a(n)+3)/2, a(1)=1
%F A006893 a(0)=1, a(n)=sum(i=0, n-1, t(a(i)), where t(n)=n*(n+1)/2. E.g. a(4)=t(1)+t(1)+t(2)+t(5)=1+1+3+15=20 
               - Jon Perry (perry(AT)globalnet.co.uk), Feb 14 2004
%p A006893 A006893 := proc(n) option remember; if n=1 then 1 else A006893(n-1)*(A006893(n-1)+3)/
               2; fi; end;
%Y A006893 Records in A057945.
%Y A006893 A007501(n-1) - 1.
%Y A006893 Sequence in context: A058109 A005331 A158872 this_sequence A003163 A088498 
               A039777
%Y A006893 Adjacent sequences: A006890 A006891 A006892 this_sequence A006894 A006895 
               A006896
%K A006893 nonn
%O A006893 1,2
%A A006893 Jeffrey Shallit
%E A006893 Additional description from Andreas M. Hinz and Daniele Parisse (hinz(AT)appl-math.tu-muenchen.de).