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A003949
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Expansion of g.f. (1+x)/(1-6*x).
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57
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1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472, 25593109080440832, 153558654482644992
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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 7.
For n >= 1, a(n+1) is equal to the number of functions f:{1,2,...,n+1}->{1,2,3,4,5,6,7} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+1} and fixed y_1, y_2,...,y_n in {1,2,3,4,5,6,7} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan Janjic, May 10 2007
For n >= 1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,2,3,5,6} 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)/(1-6*x).
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MAPLE
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k:=7; 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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q = 7; Join[{a = 1}, Table[If[n != 0, a = q*a - a, a = q*a], {n, 0, 25}]] (* or *) Join[{1}, 7*6^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-6*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
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PROG
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(Magma) k:=7; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( (1+x)/(1-6*x))); // Marius A. Burtea, Jan 20 2020
(Sage) k=7; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019
(GAP) k:=7;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 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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