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A003954
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G.f.: (1+x)/(1-11*x).
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57
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1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812
(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 12.
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
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 313
Index to divisibility sequences
Index to sequences with linear recurrences with constant coefficients, signature (11).
Index entries for sequences related to trees
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FORMULA
| a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 10 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005
G.f.: (1+x)/(1-11x). The Hankel transform of this sequence is [1,-12,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
a(0)=1; for n>0, a(n)=12*11^(n-1). [From Vincenzo Librandi,Nov 18 2010]
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MAPLE
| k := 12; if n = 0 then 1 else k*(k-1)^(n-1); fi;
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MATHEMATICA
| Join[{1}, 12*11^Range[0, 25]] (* From Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
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CROSSREFS
| Cf. A003952, A003953.
Sequence in context: A167113 A167665 A167916 * A168689 A168737 A168785
Adjacent sequences: A003951 A003952 A003953 * A003955 A003956 A003957
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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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