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Search: id:A104537
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| A104537 |
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Expansion of (1+x)/(1+2x+4x^2). |
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+0
2
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| 1, -1, -2, 8, -8, -16, 64, -64, -128, 512, -512, -1024, 4096, -4096, -8192, 32768, -32768, -65536, 262144, -262144, -524288, 2097152, -2097152, -4194304, 16777216, -16777216, -33554432, 134217728, -134217728, -268435456, 1073741824, -1073741824, -2147483648, 8589934592
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n+1) is the Hankel transform of C(2n,n)-C(2n+2,n+1). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2008
a(n+1) is the Hankel transform of C(2n,n)-2*C(n)=((n-1)/(n+1))*C(2n,n), where C(n)=A000108(n). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2008
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FORMULA
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a(n)=-2a(n-1)-4a(n-2); a(n)=2^n*cos(2*pi*n/3).
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-1)^k*3^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
a(n)=(1/2)*{[ -1+I*sqrt(3)]^n+[ -1-I*sqrt(3)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
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CROSSREFS
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Sequence in context: A079458 A138230 A128018 this_sequence A019240 A093907 A116471
Adjacent sequences: A104534 A104535 A104536 this_sequence A104538 A104539 A104540
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 13 2005
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