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A164285
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a(n) = 7*2^n + 3.
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3
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10, 17, 31, 59, 115, 227, 451, 899, 1795, 3587, 7171, 14339, 28675, 57347, 114691, 229379, 458755, 917507, 1835011, 3670019, 7340035, 14680067, 29360131, 58720259, 117440515, 234881027, 469762051, 939524099, 1879048195, 3758096387
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OFFSET
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0,1
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COMMENTS
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Contains the primes 17, 31, 59, 227, 57347, 114691, 14680067, 7516192771,..
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
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a(n) = 2*a(n-1) - 3.
a(n) = 3*a(n-1) - 2*a(n-2).
a(n) = A005009(n) + 3, a(0)=10.
G.f.: (10-13*x)/((2*x-1)*(x-1)).
E.g.f.: 7*exp(2*x) + 3*exp(x). - G. C. Greubel, Sep 12 2017
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EXAMPLE
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At n=0, a(0)=7*2^0+3=10. At n=1, a(1)=7*2^1+3=17.
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MATHEMATICA
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CoefficientList[Series[(10 - 13 x) / ((2 x - 1) (x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 12 2013 *)
LinearRecurrence[{3, -2}, {10, 17}, 40] (* Harvey P. Dale, Aug 29 2017 *)
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PROG
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(Magma) [7*2^n+3: n in [0..40]]; // Vincenzo Librandi, Sep 12 2013
(PARI) x='x+O('x^50); Vec((10-13*x)/((2*x-1)*(x-1))) \\ G. C. Greubel, Sep 12 2017
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CROSSREFS
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Sequence in context: A034097 A034107 A019991 * A268183 A293690 A069546
Adjacent sequences: A164282 A164283 A164284 * A164286 A164287 A164288
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Aug 12 2009
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EXTENSIONS
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Offset corrected by R. J. Mathar, Aug 19 2009
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STATUS
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approved
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