A083424 a(n) = (5*4^n + (-2)^n)/6.

1, 3, 14, 52, 216, 848, 3424, 13632, 54656, 218368, 873984, 3494912, 13981696, 55922688, 223698944, 894779392, 3579150336, 14316535808, 57266274304, 229064835072, 916259864576, 3665038409728, 14660155736064, 58640618749952

Offset

0,2

Comments

Binomial transform of A083423.

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (2,8).

Formula

a(n) = 2*a(n-1) + 8*a(n-2). - N. J. A. Sloane, Jul 16 2014

G.f.: (1+x)/(1-2*x-8*x^2). [Corrected by N. J. A. Sloane, Jul 16 2014]

E.g.f.: (5*exp(4*x) + exp(-2*x))/6.

From N. J. A. Sloane, Jul 18 2014: (Start)

2^(n-1)|a(n) for n >= 1;

3|a(3n+1). (End)

From Klaus Purath, Oct 15 2020: (Start)

a(n) = A048573(n)*2^(n-1).

a(n) = A048573(n)*(A048573(n+1) - A048573(n-1))/5. (End)

Example

Factorizations of initial terms: 1, (3), (2)*(7), (2)^2*(13), (2)^3*(3)^3, (2)^4*(53), (2)^5*(107), (2)^6*(3)*(71), (2)^7*(7)*(61), (2)^8*(853), (2)^9*(3)*(569), (2)^10*(3413), (2)^11*(6827), (2)^12*(3)^2*(37)*(41), (2)^13*(7)*(47)*(83), (2)^14*(13)*(4201), (2)^15*(3)*(23)*(1583), (2)^16*(218453), ...

Maple

A083424:=n->(5*4^n+(-2)^n)/6; [seq(A083424(n), n=0..50)]; # N. J. A. Sloane, Jul 18 2014

Mathematica

LinearRecurrence[{2, 8}, {1, 3}, 30] (* Harvey P. Dale, Apr 21 2019 *)

Prog

(PARI) a(n)=(5*4^n+(-2)^n)/6 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Sequence in context: A083874 A105331 A017946 * A099487 A179610 A343543

Adjacent sequences: A083421 A083422 A083423 * A083425 A083426 A083427

Keyword

easy,nonn

Author

Paul Barry, Apr 30 2003

Status

approved