login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006893 Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
(Formerly M1533)
10
1, 2, 5, 20, 230, 26795, 359026205, 64449908476890320, 2076895351339769460477611370186680, 2156747150208372213435450937462082366919951682912789656986079991220 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
M. Abert and P. Diaconis, paper in preparation, 2002.
D. Parisse, The Tower of Hanoi and the Stern-Brocot-Array, Thesis, Munich, 1997.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..13
E. Lemoine, Note sur deux nouvelles décompositions des nombres entiers, Assoc. française pour l'avancement des sciences. Vol. 29, Tome 2, pp. 72-74, 1900.
Sridhar Narayanan, The Representation Theory of 2-Sylow Subgroups of the Symmetric Group, arXiv:1712.02507 [math.RT], 2017.
FORMULA
a(n) = A007501(n-1) - 1.
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. - Jon Perry, Feb 14 2004
a(n) ~ 2 * c^(2^n), where c = 1.16007248510653786919452141287945841802404855231102953089... . - Vaclav Kotesovec, Dec 17 2014
MAPLE
A006893 := proc(n) option remember; if n=1 then 1 else A006893(n-1)*(A006893(n-1)+3)/2; fi; end;
MATHEMATICA
RecurrenceTable[{a[1] == 1, a[n] == a[n-1]*(a[n-1] + 3)/2}, a[n], {n, 10}] (* Vaclav Kotesovec, Dec 17 2014 *)
PROG
(PARI) a=vector(20); a[1]=1; for(n=2, #a, a[n]=a[n-1]*(a[n-1]+3)/2); a \\ Altug Alkan, Apr 04 2018
CROSSREFS
Where records occur in A057945, n >= 1.
Cf. A007501.
Sequence in context: A158872 A308522 A216462 * A003163 A088498 A240147
KEYWORD
nonn
AUTHOR
EXTENSIONS
Additional description from Andreas M. Hinz and Daniele Parisse
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)