OFFSET
2,1
LINKS
R. H. Hardin, Table of n, a(n) for n = 2..100
Index entries for linear recurrences with constant coefficients, signature (8,-16).
FORMULA
a(n) = (copies*n)*(copies+1)^(n-2), here: copies = 3.
Conjectures from Colin Barker, Mar 23 2018: (Start)
G.f.: 6*x*(1 - 2*x) / (1 - 4*x)^2.
a(n) = 3*4^(n-1)*(n+1).
a(n) = 8*a(n-1) - 16*a(n-2) for n>3. (End)
E.g.f.: 3*x*exp(4*x)/4. - G. C. Greubel, Jun 01 2018
From Amiram Eldar, May 16 2022: (Start)
Sum_{n>=2} 1/a(n) = (16/3)*log(4/3) - 3/2.
Sum_{n>=2} (-1)^n/a(n) = (16/3)*log(5/4) - 7/6. (End)
MATHEMATICA
LinearRecurrence[{8, -16}, {6, 36}, 30] (* or *) Table[3*n*4^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)
PROG
(PARI) for(n=2, 30, print1(3*n*4^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
(Magma) [3*n*4^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Apr 20 2009
STATUS
approved