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

2, 7, 27, 107, 427, 1707, 6827, 27307, 109227, 436907, 1747627, 6990507, 27962027, 111848107, 447392427, 1789569707, 7158278827, 28633115307, 114532461227, 458129844907, 1832519379627, 7330077518507, 29320310074027

Offset

0,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Formula

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

a(n) = A199115(n)/3.

O.g.f.: (2-3*x)/((1-x)*(1-4*x)). - R. J. Mathar, Apr 04 2008

a(n) = 5*a(n-1) - 4*a(n-2). - Vincenzo Librandi, Nov 04 2011

E.g.f.: (1/3)*(5*exp(4*x) + exp(x)). - G. C. Greubel, Jan 19 2023

Mathematica

LinearRecurrence[{5, -4}, {2, 7}, 31] (* G. C. Greubel, Jan 19 2023 *)

Prog

(Magma) [(5*4^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Nob 04 2011
(Haskell)
a136412 = (`div` 3) . (+ 1) . (* 5) . (4 ^)
-- Reinhard Zumkeller, Jun 17 2012
(PARI) a(n)=(5*4^n+1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(SageMath) [(5*4^n+1)/3 for n in range(31)] # G. C. Greubel, Jan 19 2023

Crossrefs

Sequences of the form (m*4^n + 1)/3: A007583 (m=2), this sequence (m=5), A199210 (m=11), A199210 (m=11), A206373 (m=14).

Cf. A007302, A140660, A181565, A199115.

Sequence in context: A150592 A150593 A024429 * A360149 A192417 A150594

Adjacent sequences: A136409 A136410 A136411 * A136413 A136414 A136415

Keyword

nonn,easy

Author

Paul Curtz, Mar 31 2008

Extensions

Formula in definition and more terms from R. J. Mathar, Apr 04 2008

Status

approved