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A085287
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Expansion of g.f. (1+4*x)/((1-x)*(1+x)*(1-3*x)).
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2
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1, 7, 22, 70, 211, 637, 1912, 5740, 17221, 51667, 155002, 465010, 1395031, 4185097, 12555292, 37665880, 112997641, 338992927, 1016978782, 3050936350, 9152809051, 27458427157, 82375281472, 247125844420, 741377533261, 2224132599787, 6672397799362, 20017193398090
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (-10 - 3(-1)^n + 21*3^n)/8.
a(n) = 2*a(n-1) + 3*a(n-2) + 5, a(0)=0, a(1)=1. - Zerinvary Lajos, Dec 14 2008
a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3) for n > 2.
E.g.f.: exp(x)*(9*cosh(2*x) + 12*sinh(2*x) - 5)/4. (End)
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+5 od: seq(a[n], n=1..33); # Zerinvary Lajos, Dec 14 2008
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MATHEMATICA
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LinearRecurrence[{3, 1, -3}, {1, 7, 22}, 30] (* Harvey P. Dale, Sep 22 2023 *)
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PROG
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(PARI) Vec((1+4*x)/((1-x^2)*(1-3*x)) + O(x^30)) \\ Michel Marcus, Aug 14 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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