A240526 - OEIS

%I #32 Feb 09 2024 11:15:40

%S 7,23,76,284,1072,4208,16576,65984,262912,1050368,4197376,16784384,

%T 67121152,268464128,1073790976,4295081984,17180065792,68719935488,

%U 274878693376,1099513462784,4398049656832,17592193384448,70368756760576,281475006070784,1125899957174272

%N a(n) = 2^(n-2)*(2^(n+4)-(-1)^n+13).

%H Vincenzo Librandi, <a href="/A240526/b240526.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,-16).

%F G.f.: (7-5*x-44*x^2)/(1-4*x-4*x^2+16*x^3).

%F a(n) = 4*a(n-1)+4*a(n-2)-16*a(n-3) for n>2.

%p A240526:=n->2^(n-2)*(2^(n+4)-(-1)^n+13); seq(A240526(n), n=0..30); # _Wesley Ivan Hurt_, Apr 10 2014

%t CoefficientList[Series[(7 - 5 x - 44 x^2)/(1 - 4 x - 4 x^2 + 16 x^3), {x, 0, 30}], x]

%o (Magma) [2^(n-2)*(2^(n+4)-(-1)^n+13): n in [0..25]] /* or */ I:=[7,23,76]; [n le 3 select I[n] else 4*Self(n-1)+4*Self(n-2)-16*Self(n-3): n in [1..30]];

%o (PARI) a(n)=(2^(n+4)-(-1)^n+13)<<(n-2) \\ _Charles R Greathouse IV_, Aug 26 2014

%Y Cf. A225826.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Apr 07 2014