OFFSET
8,1
LINKS
Colin Barker, Table of n, a(n) for n = 8..1000
Natasha Morrison and Alex Scott, Maximizing the number of induced cycles in a graph, Preprint, 2016. See f_2^o(n).
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,9).
FORMULA
From Chai Wah Wu, Sep 12 2016: (Start)
a(n) = 9*a(n-6) for n > 13.
G.f.: x^8*(48*x^5 + 36*x^4 + 27*x^3 + 18*x^2 + 12*x + 8)/(1 - 9*x^6). (End)
MAPLE
f:=n->
if n mod 6 = 0 then 4*3^((n-6)/3)
elif n mod 6 = 1 then 2^4*3^((n-10)/3)
elif n mod 6 = 2 then 2^3*3^((n-8)/3)
elif n mod 6 = 3 then 2^2*3^((n-6)/3)
elif n mod 6 = 4 then 2*3^((n-4)/3)
else 3^((n-2)/3); fi;
[seq(f(n), n=8..60)];
MATHEMATICA
Table[Switch[Mod[n, 6], 0, 4*3^((n - 6)/3), 1, 2^4*3^((n - 10)/3), 2, 2^3*3^((n - 8)/3), 3, 2^2*3^((n - 6)/3), 4, 2*3^((n - 4)/3), 5, 3^((n - 2)/3)], {n, 8, 50}] (* or *)
DeleteCases[CoefficientList[Series[x^8*(48 x^5 + 36 x^4 + 27 x^3 + 18 x^2 + 12 x + 8)/(1 - 9 x^6), {x, 0, 50}], x], 0] (* Michael De Vlieger, Sep 12 2016 *)
PROG
(Sage)
def A276403():
W = [8, 12, 18, 27, 36, 48]
while True:
yield W[0]
W.append(9*W.pop(0))
a = A276403();
[next(a) for _ in range(43)] # after Chai Wah Wu, Peter Luschny, Sep 12 2016
(PARI) Vec(x^8*(8+12*x+18*x^2+27*x^3+36*x^4+48*x^5)/((1-3*x^3)*(1+3*x^3)) + O(x^60)) \\ Colin Barker, Sep 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 12 2016
STATUS
approved