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A123887
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Expansion of g.f.: (1+x+x^2)/(1-5*x-5*x^2).
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2
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1, 6, 36, 210, 1230, 7200, 42150, 246750, 1444500, 8456250, 49503750, 289800000, 1696518750, 9931593750, 58140562500, 340360781250, 1992506718750, 11664337500000, 68284221093750, 399742792968750, 2340135070312500, 13699389316406250, 80197621933593750, 469485056250000000
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0)=1, a(1)=6, a(2)=36, a(n) = 5*a(n-1) + 5*a(n-2) for n>2. - Philippe Deléham, Sep 19 2009
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MAPLE
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seq(coeff(series((1+x+x^2)/(1-5*x-5*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Aug 07 2019
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MATHEMATICA
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CoefficientList[Series[(1+x+x^2)/(1-5x-5x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 5}, {1, 6, 36}, 40] (* Harvey P. Dale, Jan 03 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1+x+x^2)/(1-5*x-5*x^2)) \\ G. C. Greubel, Aug 07 2019
(Magma) I:=[6, 36]; [1] cat [n le 2 select I[n] else 5*(Self(n-1)+ Self(n-2)): n in [1..30]]; // G. C. Greubel, Aug 07 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x+x^2)/(1-5*x-5*x^2) ).list()
(GAP) a:=[6, 36];; for n in [3..30] do a[n]:=5*(a[n-1]+a[n-2]); od; Concatenation([1], a); # G. C. Greubel, Aug 07 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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STATUS
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approved
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