OFFSET
0,4
COMMENTS
Average of binomial and inverse binomial transforms of the Jacobsthal numbers A001045. - Paul Barry, Jan 04 2005
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 3.
Index entries for linear recurrences with constant coefficients, signature (2,5,-6).
FORMULA
G.f.: x*(1 - x - x^2)/((1 - x)*(1 + 2*x)*(1 - 3*x)).
a(n) = 3^n/6 - (-2)^n/6 + 1/6 - 0^n/6.
a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) for n >= 4.
a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2k)*A001045(n-2k). - Paul Barry, Jan 04 2005
E.g.f.: exp(-2*x)*(exp(5*x) + exp(3*x) - exp(2*x) - 1)/6. - Stefano Spezia, Dec 26 2021
MATHEMATICA
LinearRecurrence[{2, 5, -6}, {0, 1, 1, 6}, 30] (* Greg Dresden, Jun 19 2021 *)
PROG
(PARI) a(n) = if(n==0, 0, (3^n - (-2)^n + 1)/6) \\ Andrew Howroyd, Jun 15 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 11 2004
STATUS
approved