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Search: id:A003952
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| A003952 |
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Coordination sequence for infinite tree with valency 10. |
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+0
7
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| 1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410
(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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LINKS
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Index entries for sequences related to trees
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 311
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FORMULA
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a(n)=(10*9^n-0^n)/9. Binomial transform is A000042. - Paul Barry (pbarry(AT)wit.ie), Jan 29 2004
G.f.: (1+x)/(1-9x). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 31 2004
a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 8 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005
The Hankel transform of this sequence is [1,-10,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
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MAPLE
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k := 10; if n = 0 then 1 else k*(k-1)^(n-1); fi;
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CROSSREFS
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Sequence in context: A092420 A010579 A010576 this_sequence A033136 A061206 A137684
Adjacent sequences: A003949 A003950 A003951 this_sequence A003953 A003954 A003955
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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