OFFSET
0,2
COMMENTS
Binomial transform of A083423.
LINKS
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).
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
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 30 2003
STATUS
approved