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 A124677 Minimal total number of multiplications by single letters needed to generate all words of length n in the free monoid on two generators. 2
 0, 2, 6, 13, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE Form a tree with the empty word 0 as the root. Each node has potentially 4 children, corresponding to premultiplication by x or y and postmultiplication by x and y. Layers 0 through 3 of the tree are as follows (the edges, which just join one layer to the next, have been omitted): .............0................. .......x...........y........... ..xx.....xy.....yx....yy....... xxx xxy xyx yxx xyy yxy yyx yyy a(n) is the minimal number of edges in a subtree that includes the root and all 2^n nodes at level n. a(3) = 13 because each of xxx,xxy,xyx,xyy,yxx,yxy,yyx,yyy can be obtained in one step from xx,xy,yy; that is, we don't need yx. The corresponding subtree has 2 + 3 + 8 = 13 edges. a(4) = 27 because one computes successively: 0, x,y, xx,xy,yy, xxx,xyx,xxy,yxy,yyx,yyy and then all 16 words of length 4. CROSSREFS See A075099, A075100 for a different way of counting multiplications. Here we only grow the words one letter at a time. Sequence in context: A254821 A192953 A275970 * A034465 A182614 A288901 Adjacent sequences:  A124674 A124675 A124676 * A124678 A124679 A124680 KEYWORD more,nonn AUTHOR N. J. A. Sloane, Dec 25 2006 EXTENSIONS Definition clarified by Benoit Jubin, Jan 24 2009 STATUS approved

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Last modified December 17 00:41 EST 2018. Contains 318191 sequences. (Running on oeis4.)