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A130977
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G.f.: 5/(2 + 3*sqrt(1-20*x)).
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6
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1, 6, 66, 876, 12786, 197796, 3183156, 52718616, 892401426, 15368638836, 268388185596, 4741271556456, 84573471344916, 1521119577791976, 27554494253636136, 502257203287150896, 9205363627419463506
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OFFSET
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0,2
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COMMENTS
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Number of walks of length 2n on the 6-regular tree beginning and ending at some fixed vertex. Hankel transform is A135349. - Philippe Deléham, Feb 25 2009
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LINKS
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FORMULA
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a(n) = upper left term in M^n, M = an infinite square production matrix as follows:
6, 6, 0, 0, 0, 0, ...
5, 5, 5, 0, 0, 0, ...
5, 5, 5, 5, 0, 0, ...
5, 5, 5, 5, 5, 0, ...
5, 5, 5, 5, 5, 5, ...
... (End)
D-finite with recurrence: n*a(n) = 2*(28*n-15)*a(n-1) - 360*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 20 2012
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MATHEMATICA
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CoefficientList[Series[5/(2+3*Sqrt[1-20*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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