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A003954
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Expansion of 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
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OFFSET
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0,2
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COMMENTS
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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.
For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,11} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015
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LINKS
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FORMULA
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G.f.: (1+x)/(1-11*x). The Hankel transform of this sequence is [1,-12,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007
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MAPLE
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k:=12; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)/(1-11x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
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PROG
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(Sage) [1]+[12*11^(n-1) for n in (1..20)] # G. C. Greubel, Sep 23 2019
(GAP) Concatenation([1], List([1..20], n-> 12*11^(n-1) )); # G. C. Greubel, Sep 23 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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