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Search: id:A108474
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| A108474 |
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Expansion of 1/(1-2x)(1+4x^2)). |
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+0
1
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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).
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FORMULA
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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 (ppl(AT)spl.at), Jun 10 2008
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CROSSREFS
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Sequence in context: A120556 A120560 A003193 this_sequence A120582 A003784 A066294
Adjacent sequences: A108471 A108472 A108473 this_sequence A108475 A108476 A108477
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jun 04 2005
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