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A136412 a(n) = (5*4^n+1)/3. 7

%I

%S 2,7,27,107,427,1707,6827,27307,109227,436907,1747627,6990507,

%T 27962027,111848107,447392427,1789569707,7158278827,28633115307,

%U 114532461227,458129844907,1832519379627,7330077518507,29320310074027

%N a(n) = (5*4^n+1)/3.

%C An Engel expansion of 4/5 to the base b := 4/3 as defined in A181565, with the associated series expansion 4/5 = b/2 + b^2/(2*7) + b^3/(2*7*27) + b^4/(2*7*27*107) + .... Cf. A199115 and A140660. - _Peter Bala_, Oct 29 2013

%H Vincenzo Librandi, <a href="/A136412/b136412.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%F a(n) = 4*a(n-1)-1.

%F O.g.f.: -(-2+3*x)/((-1+x)*(-1+4*x)). - _R. J. Mathar_, Apr 04 2008

%F a(n) = 5*a(n-1)-4*a(n-2). - _Vincenzo Librandi_, Nov 04 2011

%o (MAGMA) [(5*4^n+1)/3: n in [0..30]]; // _Vincenzo Librandi_, Nob 04 2011

%o (Haskell)

%o a136412 = (`div` 3) . (+ 1) . (* 5) . (4 ^)

%o -- _Reinhard Zumkeller_, Jun 17 2012

%o (PARI) a(n)=(5*4^n+1)/3 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A007583. Cf. A007302. A140660, A181565, 1/3 of A199115.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Mar 31 2008

%E Formula in definition and more terms from _R. J. Mathar_, Apr 04 2008

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Last modified January 17 18:08 EST 2020. Contains 330987 sequences. (Running on oeis4.)