A321003 - OEIS

%I #20 Nov 02 2018 12:08:48

%S 3,22,140,856,5168,31072,186560,1119616,6718208,40310272,241863680,

%T 1451186176,8707125248,52242767872,313456640000,1880739905536,

%U 11284439564288,67706637647872,406239826411520,2437438959517696,14624633759203328,87747802559414272

%N a(n) = 2^n*(4*3^n-1).

%C Conjectured to be the sum of A175046(i) for 1 <= i < 2^(n+1).

%H Colin Barker, <a href="/A321003/b321003.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-12).

%F From _Colin Barker_, Nov 02 2018: (Start)

%F G.f.: (3 - 2*x) / ((1 - 2*x)*(1 - 6*x)).

%F a(n) = 8*a(n-1) - 12*a(n-2) for n>1.

%F (End)

%F E.g.f.: -exp(2*x)+4*exp(6*x). - _Stefano Spezia_, Nov 02 2018

%p a := n -> 2^n*(4*3^n-1):

%p seq(a(n), n = 0 .. 25); # _Stefano Spezia_, Nov 02 2018

%t a[n_]:=2^n*(4*3^n-1); Array[a, 25, 0] (* or *)

%t CoefficientList[Series[-E^(2 x) + 4 E^(6 x), {x, 0, 25}], x]*Table[k!, {k, 0, 25}] (* _Stefano Spezia_, Nov 02 2018 *)

%o (PARI) Vec((3 - 2*x) / ((1 - 2*x)*(1 - 6*x)) + O(x^25)) \\ _Colin Barker_, Nov 02 2018

%o (PARI) a(n) = 2^n*(4*3^n-1); \\ _Michel Marcus_, Nov 02 2018

%Y Cf. A175046, A171498, A321002.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Nov 01 2018