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A253208
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a(n) = 4^n + 3.
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8
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4, 7, 19, 67, 259, 1027, 4099, 16387, 65539, 262147, 1048579, 4194307, 16777219, 67108867, 268435459, 1073741827, 4294967299, 17179869187, 68719476739, 274877906947, 1099511627779, 4398046511107, 17592186044419, 70368744177667, 281474976710659
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: (4 - 13*x)/((1 - x)*(1 - 4*x)).
a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.
a(n) = 4*a(n-1) - 9 with a(0) = 4.
E.g.f.: exp(4*x) + 3*exp(x). (End)
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MATHEMATICA
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Table[4^n + 3, {n, 0, 30}] (* or *) CoefficientList[Series[(4 - 13 x) / ((1 - x) (1 - 4 x)), {x, 0, 40}], x]
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PROG
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(Magma) [4^n+3: n in [0..30]];
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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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