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
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.
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Additional description from Andreas M. Hinz and Daniele Parisse
STATUS
approved