0,3

Number of planted trees in which every node has degree <=3 and of height n; or products of height n when multiplication is commutative but non-associative.

Also called planted 3-trees or planted unary-binary trees.

The next term (which was incorrectly given) is in fact too large to include. See the b-file.

Comment from Marc LeBrun (mlb(AT)well.com): Maximum possible number of distinct new values after applying a commuting operation 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 number of elements in the n-th (n>0) 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

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

I. M. H. Etherington, On non-associative combinations, Proc. Royal Soc. Edinburgh, 59 (Part 2, 1938-39), 153-162.

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

Z. A. Melzak, A note on homogeneous dendrites, Canad. Math. Bull., 11 (1968), 85-93.

David Wasserman, Table of n, a(n) for n = 0..13

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Index entries for "core" sequences

s := proc(n) local i, j, ans; ans := [ 1 ]; for i to n do ans := [ op(ans), ans[ i ]*(add(j, j=ans)-ans[ i ])+ans[ i ]*(ans[ i ]+1)/2 ] od; RETURN(ans); end; t1 := s(10); A002658 := n->t1[n];

Cf. A006894, A005588. First differences of A072638.

Sequence in context: A053465 A024027 A079410 this_sequence A034939 A048898 A034935

Adjacent sequences: A002655 A002656 A002657 this_sequence A002659 A002660 A002661

nonn,easy,core,nice

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

Corrected by David Wasserman, Nov 20 2006