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]

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

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.

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).