A276403 a(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) otherwise 3^((n-2)/3).

8, 12, 18, 27, 36, 48, 72, 108, 162, 243, 324, 432, 648, 972, 1458, 2187, 2916, 3888, 5832, 8748, 13122, 19683, 26244, 34992, 52488, 78732, 118098, 177147, 236196, 314928, 472392, 708588, 1062882, 1594323, 2125764, 2834352, 4251528, 6377292, 9565938, 14348907, 19131876, 25509168, 38263752

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

Sequence in context: A293529 A028393 A066681 * A171241 A120137 A274951

Adjacent sequences: A276400 A276401 A276402 * A276404 A276405 A276406

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 12 2016

Status

approved