A006893 Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
1, 2, 5, 20, 230, 26795, 359026205, 64449908476890320, 2076895351339769460477611370186680, 2156747150208372213435450937462082366919951682912789656986079991220
Offset: 1
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
- Mee Seong Im and Can Ozan Oğuz, Natural transformations between induction and restriction on iterated wreath product of symmetric group of order 2, (2021).
- 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.
- Index entries for sequences related to Stern's sequences
- Index entries for sequences related to rooted trees
Programs
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Maple
A006893 := proc(n) option remember; if n=1 then 1 else A006893(n-1)*(A006893(n-1)+3)/2; fi; end;
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Mathematica
RecurrenceTable[{a[1] == 1, a[n] == a[n-1]*(a[n-1] + 3)/2}, a[n], {n, 10}] (* Vaclav Kotesovec, Dec 17 2014 *) -
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
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
Extensions
Additional description from Andreas M. Hinz and Daniele Parisse