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A003952
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G.f.: (1+x)/(1-9*x).
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57
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1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690, 1500946352969991210, 13508517176729920890
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Coordination sequence for infinite tree with valency 10.
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
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 311
Index to divisibility sequences
Index to sequences with linear recurrences with constant coefficients, signature (9).
Index entries for sequences related to trees
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FORMULA
| a(n)=(10*9^n-0^n)/9. Binomial transform is A000042. - Paul Barry, Jan 29 2004
G.f.: (1+x)/(1-9x). - DELEHAM Philippe, Jan 31 2004
a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 8 . - Philippe DELEHAM, Jul 10 2005
The Hankel transform of this sequence is [1,-10,0,0,0,0,0,0,0,...]. - Philippe DELEHAM, Nov 21 2007
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MAPLE
| k := 10; if n = 0 then 1 else k*(k-1)^(n-1); fi;
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MATHEMATICA
| Join[{1}, 10*9^Range[0, 25]] (* From Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
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PROG
| (MAGMA) [(10*9^n-0^n)/9: n in [0..20] ]; // Vincenzo Librandi, Aug 19 2011
(PARI) a(n)=10*9^n\9 \\ Charles R Greathouse IV, Sep 08 2011
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CROSSREFS
| Cf. A003949, A003950, A003951.
Sequence in context: A170595 A170643 A170691 * A033136 A061206 A199527
Adjacent sequences: A003949 A003950 A003951 * A003953 A003954 A003955
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2009.
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