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A006893 Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
(Formerly M1533)
7
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

Table of n, a(n) for n=1..10.

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. E.g., a(4) = t(1) + t(1) + t(2) + t(5) = 1 + 1 + 3 + 15 = 20. - 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: A261005 A158872 A216462 * A003163 A088498 A240147

Adjacent sequences:  A006890 A006891 A006892 * 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)

STATUS

approved

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Last modified December 13 22:07 EST 2018. Contains 318087 sequences. (Running on oeis4.)