A083584 a(n) = (8*4^n - 5)/3.

1, 9, 41, 169, 681, 2729, 10921, 43689, 174761, 699049, 2796201, 11184809, 44739241, 178956969, 715827881, 2863311529, 11453246121, 45812984489, 183251937961, 733007751849, 2932031007401, 11728124029609, 46912496118441

Offset

0,2

Comments

a(n) = A007583(n+1) - 2 = A020988(n) - 1 = A039301(n+2) - 3. - Ralf Stephan, Jun 14 2003

Sum of n-th row of triangle of powers of 4: 1; 4 1 4; 16 4 1 4 16; 64 16 4 1 4 16 64; .... - Philippe Deléham, Feb 24 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..170

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

Formula

a(n) = (8*4^n - 5)/3.

G.f.: (1+4*x)/((1-x)*(1-4*x)).

E.g.f.: (8*exp(4*x) - exp(x))/3.

a(0)=1, a(1)=9, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Oct 23 2011

a(n) = 4*a(n-1) + 5, a(0) = 1. - Philippe Deléham, Feb 24 2014

a(n+1) = 2^(2^n+1) + a(n), a(1)=1. - Ben Paul Thurston, Dec 27 2015

Example

a(0) = 1;
a(1) = 4 + 1 + 4 = 9;
a(2) = 16 + 4 + 1 + 4 + 16 = 41;
a(3) = 64 + 16 + 4 + 1 + 4 + 16 + 64 = 169; etc. - Philippe Deléham, Feb 24 2014

Mathematica

(8 4^Range[0, 30]-5)/3 (* or *) LinearRecurrence[{5, -4}, {1, 9}, 30] (* Harvey P. Dale, Oct 23 2011 *)

Prog

(Magma) [(8*4^n-5)/3: n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011
(PARI) a(n)=(8*4^n-5)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Python) print([8*4**n//3 - 1 for n in range(50)]) # Karl V. Keller, Jr., May 21 2022

Crossrefs

Cf. A083855.

Sequence in context: A034441 A201275 A056243 * A276780 A183916 A199311

Adjacent sequences: A083581 A083582 A083583 * A083585 A083586 A083587

Keyword

easy,nonn

Author

Paul Barry, May 01 2003

Status

approved