A247281 - OEIS

%I #33 Jun 29 2023 11:29:53

%S 0,5,15,65,255,1025,4095,16385,65535,262145,1048575,4194305,16777215,

%T 67108865,268435455,1073741825,4294967295,17179869185,68719476735,

%U 274877906945,1099511627775,4398046511105,17592186044415

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

%H OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,4).

%F a(n) = 5*A015521(n).

%F a(n+1) = 10*A037481(n) + 5.

%F a(n+1) = 4*a(n) + 5*(-1)^n.

%F a(n) = 3*a(n-1) + 4*a(n-2). - _Colin Barker_, Sep 11 2014

%F G.f.: -5*x / ((x+1)*(4*x-1)). - _Colin Barker_, Sep 11 2014

%t LinearRecurrence[{3, 4}, {0, 5}, 23] (* _Jean-François Alcover_, May 22 2016 *)

%o (PARI) concat(0, Vec(-5*x / ((x+1)*(4*x-1)) + O(x^100))) \\ _Colin Barker_, Sep 11 2014

%o (PARI) vector(100,n,4^(n-1)+(-1)^n) \\ _Derek Orr_, Sep 11 2014

%o (Python)

%o def A247281(n): return (1<<(n<<1))+(1 if n&1 else -1) # _Chai Wah Wu_, Jun 28 2023

%Y Cf. A015521, A037481, A084623.

%K nonn,easy,less

%O 0,2

%A _Paul Curtz_, Sep 11 2014

%E Typos in data fixed by _Colin Barker_, Sep 11 2014