A138340 - OEIS

%I #18 Jan 25 2026 04:00:54

%S 1,-4,-32,-64,256,2048,4096,-16384,-131072,-262144,1048576,8388608,

%T 16777216,-67108864,-536870912,-1073741824,4294967296,34359738368,

%U 68719476736,-274877906944,-2199023255552,-4398046511104,17592186044416,140737488355328,281474976710656,-1125899906842624

%N Expansion of (1-8*x)/(1-4*x+16*x^2).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-16).

%F abs(a(n)) = 2^A047267(n).

%F a(n) = 2*4^n(cos(Pi*(n+1)/3) - sqrt(3)*sin(Pi*(n+1))/3).

%F a(n) = 4^n*Sum_{k=0..n} A121314(n,k)*(-1)^k*3^(n-k). - _Philippe Deléham_, Nov 01 2008

%F a(n) = A128018(n)*2^n. - _Philippe Deléham_, Nov 14 2008

%F a(n) = 4*a(n-1) - 16*a(n-2); a(0)=1, a(1)=-4. - _Harvey P. Dale_, Sep 30 2014

%F From _Amiram Eldar_, Jan 25 2026: (Start)

%F Sum_{n>=0} 1/a(n) = 46/65.

%F Sum_{n>=0} (-1)^n/a(n) = 26/21. (End)

%t CoefficientList[Series[(1-8x)/(1-4x+16x^2),{x,0,30}],x] (* or *) LinearRecurrence[{4,-16},{1,-4},30] (* _Harvey P. Dale_, Sep 30 2014 *)

%Y Cf. A047267, A121314, A128018.

%K easy,sign

%O 0,2

%A _Paul Barry_, Mar 15 2008

%E More terms from _Amiram Eldar_, Jan 25 2026