A080643 a(0)=0; for n>0, a(n) = 4^n - 2*3^(n-1).

0, 2, 10, 46, 202, 862, 3610, 14926, 61162, 249022, 1009210, 4076206, 16422922, 66045982, 265246810, 1064175886, 4266269482, 17093775742, 68461196410, 274103065966, 1097187104842, 4391072942302, 17571265338010, 70305982058446, 281286690353002, 1125335047769662

Offset: 0

Author

Max Alekseyev, Feb 26 2003

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-12).

Crossrefs

Complement of A025192 in 4^n.

Programs

Mathematica

Join[{0},Table[4^n-2*3^(n-1),{n,30}]] (* or *) LinearRecurrence[{7,-12},{0,2,10},30] (* Harvey P. Dale, Dec 29 2023 *)

Python

def A080643(n): return (1<<(n<<1))-(3**(n-1)<<1) if n else 0 # Chai Wah Wu, Apr 02 2025

Formula

G.f.: 2*x*(1-2*x)/((1-3*x)*(1-4*x)). - Colin Barker, Jan 20 2012

E.g.f.: (3*exp(4*x) - 2*exp(3*x) - 1)/3. - Stefano Spezia, Apr 03 2025