OFFSET
0,2
LINKS
FORMULA
Binomial transform of A133125.
G.f.: (1 + 3*x)/(1 - 2*x - 8*x^2).
E.g.f.: (1/3)*exp(x)*(3*exp(3*x) + sinh(3*x)).
a(n) = 2*a(n-1) + 8*a(n-2), for n > 1.
a(n) = 4*a(n-1) + (-2)^n, for n > 0.
a(n) = (a(n+2) - 2*a(n+1))/8.
From Thomas Scheuerle, Jul 03 2024: (Start)
a(n) = 2^(n - 1)*((-1)^(n + 1) + 7*2^n)/3.
a(n) = A003683(n) + 4^n.
Binomial transform: A108982.
MATHEMATICA
LinearRecurrence[{2, 8}, {1, 5}, 27] (* Amiram Eldar, Jul 03 2024 *)
PROG
(PARI) a(n) = 2^(n-1)*((-1)^(n+1) + 7*2^n)/3 \\ Thomas Scheuerle, Jul 03 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jul 03 2024
STATUS
approved