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Search: id:A003950
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| A003950 |
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Coordination sequence for infinite tree with valency 8. |
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+0
7
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| 1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The n-th term of the coordination sequence of the infinite tree with valency 2m is the same as the number of reduced words of size n in the free group on m generators. In the five sequences A003946, A003948, A003950, A003952, A003954 m is 2, 3, 4, 5, 6 . - Avi Peretz (njk(AT)netvision.net.il), Feb 23 2001 and Ola Veshta (olaveshta(AT)my-deja.com), Mar 30 2001.
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REFERENCES
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A. M. Nemirovsky et al., Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 309
Index entries for sequences related to trees
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FORMULA
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a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 6 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005
a(n)=8*7^(n-1)for n>=1, a(0)=1 . G.f.: (1+x)/(1-7x). The Hankel transform of this sequence is [1,-8,0,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
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MAPLE
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k := 8; if n = 0 then 1 else k*(k-1)^(n-1); fi;
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CROSSREFS
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Sequence in context: A010556 A010575 A063812 this_sequence A033134 A126985 A027081
Adjacent sequences: A003947 A003948 A003949 this_sequence A003951 A003952 A003953
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KEYWORD
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nonn,walk
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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