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A146963
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a(n) = ((3 + sqrt(7))^n + (3 - sqrt(7))^n)/2.
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5
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1, 3, 16, 90, 508, 2868, 16192, 91416, 516112, 2913840, 16450816, 92877216, 524361664, 2960415552, 16713769984, 94361788800, 532743192832, 3007735579392, 16980927090688, 95870091385344, 541258694130688
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OFFSET
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0,2
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COMMENTS
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Inverse binomial transform of A146964.
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=3.
G.f.: (1-3*x)/(1-6*x+2*x^2). (End)
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MAPLE
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seq(coeff(series((1-3*x)/(1-6*x+2*x^2), x, n+1), x, n), n = 0..25); # G. C. Greubel, Jan 08 2020
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MATHEMATICA
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Transpose[NestList[Join[{Last[#], 6Last[#]-2First[#]}]&, {1, 3}, 25]] [[1]] (* or *) CoefficientList[Series[(1-3x)/(1-6x+2x^2), {x, 0, 25}], x] (* Harvey P. Dale, Apr 11 2011 *)
LinearRecurrence[{6, -2}, {1, 3}, 25] (* G. C. Greubel, Jan 08 2020 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((3+r7)^n+(3-r7)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008
(PARI) my(x='x+O('x^25)); Vec((1-3*x)/(1-6*x+2*x^2)) \\ G. C. Greubel, Jan 08 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-3*x)/(1-6*x+2*x^2) ).list()
(GAP) a:=[1, 3];; for n in [3..25] do a[n]:=6*a[n-1]-2*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008
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EXTENSIONS
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STATUS
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approved
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