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A123010
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a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3), for n>4, with a(1)=1, a(2)=0, a(3)=4, a(4)=16.
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1
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1, 0, 4, 16, 84, 416, 2084, 10416, 52084, 260416, 1302084, 6510416, 32552084, 162760416, 813802084, 4069010416, 20345052084, 101725260416, 508626302084, 2543131510416, 12715657552084, 63578287760416, 317891438802084
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OFFSET
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1,3
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LINKS
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FORMULA
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O.g.f.: (1 -4*x -x^2)/((1+x)*(1-5*x)). - R. J. Mathar, Dec 05 2007
a(n) = (1/3)*(2*5^(n-2) - 2*(-1)^n) + (1/5)*0^(n-1). - Ridouane Oudra, Feb 22 2021
E.g.f.: (1/75)*(48 + 158x - 50*exp(-x) + 2*exp(5*x)). - G. C. Greubel, Jul 13 2021
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MATHEMATICA
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LinearRecurrence[{5, 1, -5}, {1, 0, 4, 16}, 40] (* G. C. Greubel, Jul 13 2021 *)
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PROG
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(PARI) my(x='x+O('x^33)); Vec((x^2+4*x-1)/((x+1)*(5*x-1))) \\ Joerg Arndt, Feb 22 2021
(Sage) [1]+[(2/3)*(5^(n-2) - (-1)^n) for n in (2..40)] # G. C. Greubel, Jul 13 2021
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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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EXTENSIONS
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STATUS
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approved
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