A083597 a(n) = (7*4^n - 4)/3.

1, 8, 36, 148, 596, 2388, 9556, 38228, 152916, 611668, 2446676, 9786708, 39146836, 156587348, 626349396, 2505397588, 10021590356, 40086361428, 160345445716, 641381782868, 2565527131476, 10262108525908, 41048434103636

Offset: 0

Author

Paul Barry, May 02 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A082541.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Programs

Magma

[(7*4^n-4)/3: n in [0..25]]; // Vincenzo Librandi, Jul 24 2011

Mathematica

(7*4^Range[0,25]-4)/3 (* or *) LinearRecurrence[{5,-4},{1,8},26] (* Harvey P. Dale, Jul 23 2011 *)
CoefficientList[Series[(1 + 3 x)/((1 - 4 x) (1 - x)), {x, 0, 22}], x] (* Michael De Vlieger, Mar 03 2017 *)

PARI

a(n)=(7*4^n-4)/3 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (7*4^n-4)/3.

G.f.: (1+3*x)/((1-4*x)*(1-x)).

E.g.f.: (7*exp(4*x)-4*exp(x))/3.

a(n) = 4*a(n-1) + 4, n > 0. - Gary Detlefs, Jun 23 2010

a(0)=1, a(1)=8, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Jul 23 2011

a(n) = A020988(n) + A020989(n), n >= 0. - Yosu Yurramendi, Mar 03 2017