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A167031
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a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.
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5
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1, 20, 337, 5461, 87653, 1403557, 22461349, 359399333, 5750460325, 92007649189, 1472123522981, 23553980911525, 376863712759717, 6029819476856741, 96477111920512933, 1543633791891427237, 24698140674915717029
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OFFSET
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0,2
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COMMENTS
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lim_{n -> infinity} a(n)/a(n-1) = 16.
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LINKS
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FORMULA
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a(n) = (241*16^n - 65*4^n + 4)/180.
G.f.: (1-x+x^2)/((1-x)*(1-4*x)*(1-16*x)).
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-2).
E.g.f.: (1/180)*(241*exp(16*x) - 65*exp(4*x) + 4*exp(x)). (End)
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MATHEMATICA
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LinearRecurrence[{21, -84, 64}, {1, 20, 337}, 50] (* G. C. Greubel, May 30 2016 *)
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PROG
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(Magma) [ n le 2 select 19*n-18 else 20*Self(n-1)-64*Self(n-2)+1: n in [1..17] ];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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