OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (-1,2,2).
FORMULA
E.g.f.: 2*cosh(sqrt(2)*x) + 2*sinh(sqrt(2)*x)/sqrt(2) - sinh(x) + cosh(x).
a(n) = (1 + 1/sqrt(2))*sqrt(2)^n + (1 - 1/sqrt(2))*(-sqrt(2))^n - (-1)^n.
G.f.: (1+2*x)^2/((1+x)*(1-2*x^2)). - Colin Barker, Aug 17 2012
a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3); a(0)=1, a(1)=3, a(2)=3. - Harvey P. Dale, Mar 10 2013
From Amiram Eldar, Sep 14 2022: (Start)
Sum_{n>=0} (-1)^n/a(n) = 2 * A248721. (End)
MATHEMATICA
CoefficientList[Series[(1+2x)^2/((1+x)(1-2x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[ {-1, 2, 2}, {1, 3, 3}, 50] (* Harvey P. Dale, Mar 10 2013 *)
PROG
(Magma) [2*2^Floor(n/2)-(-1)^n: n in [0..40]]; // Vincenzo Librandi, Aug 16 2011
(PARI) vector(40, n, n--; 2^(floor(n/2)+1) - (-1)^n) \\ G. C. Greubel, Nov 08 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 16 2003
STATUS
approved