OFFSET
0,3
COMMENTS
This sequence belongs to a family of sequences with GF(x) = (1+(k+2)*x+(2*k-4)*x^2)/(1-2*x-(k+8)*x^2-(2*k)*x^3). Among the members of this family are several red king sequences, see A179597. For the sequence given above, which is not a red king sequence, k = -4.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2, 4, -8).
FORMULA
GF(x) = (1-2*x-12*x^2)/(1-2*x-4*x^2+8*x^3)
a(n) = 2*a(n-1)+4*a(n-2)-8*a(n-3) with a(1)=1, a(2)=0 and a(3)=-8.
a(n) = (5-(-1)^n-6*n)*2^(n-2)
MATHEMATICA
Table[(5-(-1)^n-6n)2^(n-2), {n, 0, 30}] (* or *) LinearRecurrence[{2, 4, -8}, {1, 0, -8}, 30] (* Harvey P. Dale, Mar 25 2021 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Johannes W. Meijer, Jul 28 2010
STATUS
approved