1,2

Representation requires n triangular numbers with greedy algorithm.

Comment from Marc LeBrun (mlb(AT)well.com): Maximum possible number of distinct values after applying a commuting operation from 0 to N times to a single initial value.

Divide the natural numbers in sets of consecutive numbers, starting with {1}, each set with number of elements equal to the sum of elements of the preceding set. The greatest element of the n-th set gives a(n). The sets begin {1}, {2}, {3,4}, {5,6,7,8,9,10,11}, ... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jan 16 2002

a(n+1) = (a(n)) th triangular numbers + 1 = A000217(a(n)) + 1. a(n) = A072638(n-1) + 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 11 2009]

F. Harary et al., Counting free binary trees..., J. Combin. Inform. System Sciences, 17 (1992), 175-181.

E. Lemoine, ``Note sur deux nouvelles d\'{e}compositions des nombres entiers,'' Assoc. fran\c{c}aise pour l'avancement des sciences. Vol. 29, pp. 72-74, 1900.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

David Wasserman, Table of n, a(n) for n = 1..14

Index entries for "core" sequences

Index entries for sequences related to rooted trees

Partial sums of A002658; a(n+1) = a(n)(a(n)+1)/2 + 1 (from Marc LeBrun).

Sequence arises from a self-recursive process: a[1]=1, a[n]=a[n-1]*(a[n-1]+1)/2+1. E.g. a(1)=1, a(2)=1*2/2+1=2, a(3)=2*3/2+1=4, a(4)=4*5/2+1=11, a(5)=11*12/2+1=67... - Miklos Kristof (kristmikl(AT)freemail.hu), Dec 11 2007

A006894 := proc(n) option remember; if n=1 then 1 else A006894(n-1)*(A006894(n-1)+1)/2+1 fi end; [ seq(A006894(i), i=1..11) ];

a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n-1]+2, 2) od: seq(a[n]+1, n=-1..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 08 2007

a[1]:=1:for n from 2 to 10 do a[n]:=a[n-1]*(a[n-1]+1)/2+1 od: seq(a[n], n=1..10); - Miklos Kristof (kristmikl(AT)freemail.hu), Dec 11 2007

Row sums of A036602.

Sequence in context: A091233 A156434 A007903 this_sequence A038093 A057284 A156463

Adjacent sequences: A006891 A006892 A006893 this_sequence A006895 A006896 A006897

nonn,easy,core,nice

Jeffrey Shallit, N. J. A. Sloane (njas(AT)research.att.com).