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A081336
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a(n) = (7^n + 3^n)/2.
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7
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1, 5, 29, 185, 1241, 8525, 59189, 412865, 2885681, 20186645, 141267149, 988751945, 6920909321, 48445302365, 339113927909, 2373787929425, 16616486808161, 116315321563685, 814206992665469, 5699448173817305, 39896134892198201
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OFFSET
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0,2
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COMMENTS
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5th binomial transform of (1,0,4,0,16,0,64,...).
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 21*a(n-2), a(0)=1, a(1)=5.
G.f.: (1-5*x)/((1-3*x)*(1-7*x)).
E.g.f.: exp(5*x) * cosh(2*x).
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MATHEMATICA
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CoefficientList[Series[(1 - 5 x) / ((1 - 3 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *)
LinearRecurrence[{10, -21}, {1, 5}, 30] (* Harvey P. Dale, Dec 07 2014 *)
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PROG
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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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