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A135583
a(n) = 4*a(n-1) - 4 for n>0, a(0)=3.
1
3, 8, 28, 108, 428, 1708, 6828, 27308, 109228, 436908, 1747628, 6990508, 27962028, 111848108, 447392428, 1789569708, 7158278828, 28633115308, 114532461228, 458129844908, 1832519379628, 7330077518508, 29320310074028
OFFSET
0,1
FORMULA
From R. J. Mathar, Mar 31 2008: (Start)
a(n) = (4 + 5*4^n)/3.
a(n) - a(n-1) = A003947(n).
O.g.f.: (3 - 7*x)/((1 - x)*(1 - 4*x)). (End)
a(0)=3, a(1)=8; for n>1, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Feb 27 2013
E.g.f.: (1/3)*(4*exp(x) + 5*exp(4*x)). - G. C. Greubel, Oct 20 2016
MATHEMATICA
NestList[4#-4&, 3, 30] (* or *) LinearRecurrence[{5, -4}, {3, 8}, 30] (* Harvey P. Dale, Feb 27 2013 *)
PROG
(Magma) [(4+5*4^n)/3: n in [0..30]]; // Vincenzo Librandi, Aug 10 2011
CROSSREFS
Cf. A003947.
Sequence in context: A263103 A093356 A224271 * A317077 A009437 A347072
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 25 2008
EXTENSIONS
More terms from R. J. Mathar, Mar 31 2008
STATUS
approved