A006893 Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n. (Formerly M1533)

1, 2, 5, 20, 230, 26795, 359026205, 64449908476890320, 2076895351339769460477611370186680, 2156747150208372213435450937462082366919951682912789656986079991220

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.

Index entries for sequences related to Stern's sequences

Index entries for sequences related to rooted trees

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

Adjacent sequences: A006890 A006891 A006892 * A006894 A006895 A006896

Keyword

nonn,easy

Author

Jeffrey Shallit

Extensions

Additional description from Andreas M. Hinz and Daniele Parisse

Status

approved