A276403 - OEIS

%I #21 Mar 01 2020 15:24:02

%S 8,12,18,27,36,48,72,108,162,243,324,432,648,972,1458,2187,2916,3888,

%T 5832,8748,13122,19683,26244,34992,52488,78732,118098,177147,236196,

%U 314928,472392,708588,1062882,1594323,2125764,2834352,4251528,6377292,9565938,14348907,19131876,25509168,38263752

%N 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).

%H Colin Barker, <a href="/A276403/b276403.txt">Table of n, a(n) for n = 8..1000</a>

%H Natasha Morrison and Alex Scott, <a href="https://people.maths.ox.ac.uk/scott/Papers/maxinduced.pdf">Maximizing the number of induced cycles in a graph</a>, Preprint, 2016. See f_2^o(n).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,9).

%F From _Chai Wah Wu_, Sep 12 2016: (Start)

%F a(n) = 9*a(n-6) for n > 13.

%F G.f.: x^8*(48*x^5 + 36*x^4 + 27*x^3 + 18*x^2 + 12*x + 8)/(1 - 9*x^6). (End)

%p f:=n->

%p if n mod 6 = 0 then 4*3^((n-6)/3)

%p elif n mod 6 = 1 then 2^4*3^((n-10)/3)

%p elif n mod 6 = 2 then 2^3*3^((n-8)/3)

%p elif n mod 6 = 3 then 2^2*3^((n-6)/3)

%p elif n mod 6 = 4 then 2*3^((n-4)/3)

%p else 3^((n-2)/3); fi;

%p [seq(f(n),n=8..60)];

%t 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 *)

%t 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 *)

%o (Sage)

%o def A276403():

%o     W = [8, 12, 18, 27, 36, 48]

%o     while True:

%o         yield W[0]

%o         W.append(9*W.pop(0))

%o a = A276403();

%o [next(a) for _ in range(43)] # after _Chai Wah Wu_, _Peter Luschny_, Sep 12 2016

%o (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

%K nonn,easy

%O 8,1

%A _N. J. A. Sloane_, Sep 12 2016