OFFSET
0,2
COMMENTS
This sequence belongs to a family of sequences with g.f. (1+x)/(1 - 2*x - (k+8)*x^2 - 2*k*x^3). Among the members of this family are several red king sequences, see A179596. For the sequence given above, which is not a red king sequence, k = -4.
Inverse binomial transform of A119916 (without the leading 0).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 4, -8).
FORMULA
G.f.: (1+x)/(1 - 4*x^2 - 2*x + 8*x^3).
a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3) with a(1)=1, a(2)=3 and a(3)=10.
a(n) = (7 + (-1)^n + 6*n)*2^(n-3).
PROG
(Magma) [(7+(-1)^n+6*n)*2^(n-3): n in [0..30]]; // Vincenzo Librandi, Jul 18 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Jul 28 2010
STATUS
approved