|
Search: id:A006893
|
|
|
| A006893 |
|
Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
(Formerly M1533)
|
|
+0
5
|
|
| 1, 2, 5, 20, 230, 26795, 359026205, 64449908476890320, 2076895351339769460477611370186680, 2156747150208372213435450937462082366919951682912789656986079991220
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
M. Abert and P. Diaconis, paper in preparation, 2002.
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. Parisse, The Tower of Hanoi and the Stern-Brocot-Array, Thesis, Munich, 1997.
|
|
LINKS
|
Index entries for sequences related to Stern's sequences
Index entries for sequences related to rooted trees
|
|
FORMULA
|
a(n+1) = a(n)*(a(n)+3)/2, a(1)=1
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
|
|
MAPLE
|
A006893 := proc(n) option remember; if n=1 then 1 else A006893(n-1)*(A006893(n-1)+3)/2; fi; end;
|
|
CROSSREFS
|
Records in A057945.
A007501(n-1) - 1.
Sequence in context: A111885 A058109 A005331 this_sequence A003163 A088498 A039777
Adjacent sequences: A006890 A006891 A006892 this_sequence A006894 A006895 A006896
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jeffrey Shallit
|
|
EXTENSIONS
|
Additional description from Andreas M. Hinz and Daniele Parisse (hinz(AT)appl-math.tu-muenchen.de).
|
|
|
Search completed in 0.002 seconds
|
