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A108474 Expansion of 1/(1-2x)(1+4x^2)). 1
1, 2, 0, 0, 16, 32, 0, 0, 256, 512, 0, 0, 4096, 8192, 0, 0, 65536, 131072, 0, 0, 1048576, 2097152, 0, 0, 16777216, 33554432, 0, 0, 268435456, 536870912, 0, 0, 4294967296, 8589934592, 0, 0, 68719476736, 137438953472, 0, 0, 1099511627776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

2^n with gaps. In general, sum{k=0..n, sum{j=0..n, C(2(n-k),j)C(2k,j)r^j}} has expansion (1-(r+1)x)/((1+(r+3)x+(r-1)(r+3)x^2+(r-1)^3*x^3).

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (2,-4,8).

FORMULA

G.f.:1/(1-2x+4x^2-8x^3); a(n)=2a(n-1)-4a(n-2)+8a(n-3); a(n)=sum{k=0..n, sum{j=0..n, C(2(n-k), j)C(2k, j)(-1)^j}}.

a(n)=(1/2)*2^n+[1/4+(1/4)*I]*(-2*I)^n+[1/4-(1/4)*I]*(2*I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 10 2008

CROSSREFS

Sequence in context: A120560 A158465 A003193 * A120582 A003784 A244143

Adjacent sequences:  A108471 A108472 A108473 * A108475 A108476 A108477

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 04 2005

STATUS

approved

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Last modified September 22 14:14 EDT 2020. Contains 337291 sequences. (Running on oeis4.)