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A168617
a(n) = 7*2^(n-1) - 2*n - 5.
1
0, 5, 17, 43, 97, 207, 429, 875, 1769, 3559, 7141, 14307, 28641, 57311, 114653, 229339, 458713, 917463, 1834965, 3669971, 7339985, 14680015, 29360077, 58720203, 117440457, 234880967, 469761989, 939524035, 1879048129, 3758096319
OFFSET
1,2
FORMULA
a(n) = 2*a(n-1) + 2*n + 1 (with a(1)=0).
From Colin Barker, Sep 18 2012: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
G.f.: x^2*(5 - 3*x)/(1 - 4*x + 5*x^2 - 2*x^3). (End)
E.g.f.: (1/2)*(3 - (10 + 4*x)*exp(x) + 7*exp(2*x)). - G. C. Greubel, Jul 27 2016
MATHEMATICA
Table[(7*2^(n-1) - 2*n - 5), {n, 1, 40}] (* Vincenzo Librandi, Sep 18 2012 *)
LinearRecurrence[{4, -5, 2}, {0, 5, 17}, 25] (* G. C. Greubel, Jul 27 2016 *)
PROG
(Magma) I:=[0, 5, 17]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Sep 18 2012
CROSSREFS
Sequence in context: A146640 A100705 A100662 * A046916 A089527 A146778
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 01 2009
EXTENSIONS
Definition and examples simplified by Jon E. Schoenfield, Jun 19 2010
STATUS
approved