A119332 - OEIS

%I #7 Jul 21 2024 15:18:41

%S 1,1,0,0,2,2,0,0,4,4,0,0,8,8,0,0,16,16,0,0,32,32,0,0,64,64,0,0,128,

%T 128,0,0,256,256,0,0,512,512,0,0,1024,1024,0,0,2048,2048,0,0,4096,

%U 4096,0,0,8192,8192,0,0,16384,16384,0,0,32768

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

%C Row sums of A119331. Binomial transform is A119330.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2).

%F a(n)=sum{k=0..n, sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)*2^j}}}.

%t CoefficientList[Series[(1+x)/(1-2x^4),{x,0,90}],x] (* or *) LinearRecurrence[{0,0,0,2},{1,1,0,0},90] (* _Harvey P. Dale_, Jul 21 2024 *)

%K easy,nonn

%O 0,5

%A _Paul Barry_, May 14 2006