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Search: id:A063895
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| A063895 |
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Start with x, xy; then concatenate each word in turn with all preceding words, getting x xy xxy xxxy xyxxy xxxxy xyxxxy xxyxxxy ...; sequence gives number of words of length n. Also binary trees by degree: x (x,y) (x,(x,y)) (x,(x,(x,y))) ((x,y),(x,(x,y)))... |
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+0
5
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| 1, 1, 1, 1, 2, 3, 6, 11, 22, 43, 88, 179, 372, 774, 1631, 3448, 7347, 15713, 33791, 72923, 158021, 343495, 749102, 1638103, 3591724, 7893802, 17387931, 38379200, 84875596, 188036830, 417284181, 927469845, 2064465341, 4601670625
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Also binary rooted identity trees (those with no symmetries).
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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f(n)=(sum f(i).f(j), i+j=n, i<j)+(if n=2k, (f(k)-1).f(k)/2), f(1)=1, f(2)=1.
G.f. A(x)=1-sqrt(1-2x-2x^2+A(x^2)) satisfies x+x^2-A(x)+(A(x)^2-A(x^2))/2=0, A(0)=0. - Michael Somos, Sep 06 2003
a(n)=(sum a(i)a(j), i+j=n, i<j)+(if n=2k, (a(k)-1)a(k)/2), n>2. a(1)=a(2)=1.
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PROGRAM
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(PARI) {a(n)=local(A, m); if(n<1, 0, m=1; A=O(x); while( m<=n, m*=2; A=1-sqrt(1-2*x-2*x^2+subst(A, x, x^2))); polcoeff(A, n))}
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CROSSREFS
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Cf. A001190, A063894, A036774.
Adjacent sequences: A063892 A063893 A063894 this_sequence A063896 A063897 A063898
Sequence in context: A005578 A058050 A026418 this_sequence A027214 A132831 A007477
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KEYWORD
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easy,nonn,nice,eigen
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AUTHOR
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Claude Lenormand (claude.lenormand(AT)free.fr), Aug 29 2001
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EXTENSIONS
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Additional comments and g.f. from Christian G. Bower (bowerc(AT)usa.net), Nov 29 2001
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