A119332 Expansion of (1+x)/(1-2x^4).

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, 128, 0, 0, 256, 256, 0, 0, 512, 512, 0, 0, 1024, 1024, 0, 0, 2048, 2048, 0, 0, 4096, 4096, 0, 0, 8192, 8192, 0, 0, 16384, 16384, 0, 0, 32768

Offset: 0

Author

Paul Barry, May 14 2006

Keywords

• easy
• nonn

Comments

Row sums of A119331. Binomial transform is A119330.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2).

Programs

Mathematica

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 *)

Formula

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}}}.