OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
FORMULA
From R. J. Mathar, Oct 21 2008: (Start)
G.f.: 6*x/((1-2*x)*(1-x)*(1+x)).
a(n) = 2^(n+2) - 3 - (-1)^n. (End)
a(n) ~ 4*2^n. - Charles R Greathouse IV, May 31 2026
From Elmo R. Oliveira, Aug 23 2026: (Start)
E.g.f.: 2*(2*exp(2*x) - 2*cosh(x) - sinh(x)). (End)
MATHEMATICA
Table[2^(n+2)-3-(-1)^n, {n, 0, 40}] (* Vincenzo Librandi, Apr 03 2012 *)
(* Alternative: *)
CoefficientList[Series[6x/((1-2x)(1-x)(1+x)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 03 2012 *)
(* Alternative: *)
nxt[{n_, a_}]:={n+1, If[EvenQ[n], 2a, 2a+6]}; NestList[nxt, {1, 0}, 40][[;; , 2]] (* Harvey P. Dale, Aug 26 2024 *)
(* Alternative: *)
LinearRecurrence[ {2, 1, -2}, {0, 6, 12}, 40] (* Harvey P. Dale, Aug 26 2024 *)
PROG
(Magma) [2^(n+2)-3-(-1)^n: n in [0..30]]; // Vincenzo Librandi, Apr 03 2012
(PARI) a(n)=4*2^n-3-(-1)^n \\ Charles R Greathouse IV, May 31 2026
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved