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Search: id:A138230
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| A138230 |
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Expansion of (1-x)/(1-2x+4x^2). |
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+0
4
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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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In general, the expansion of (1-x)/(1-2x+(m+1)x^2) has general term given by a(n)=sum{k=0..floor(n/2), C(n,2k)(-m)^k}=((1+sqrt(-m))^n+(1-sqrt(-m))^n)/2.
Binomial transform of [1, 0, -3, 0, 9, 0, -27, 0, 81, 0, ...]=: powers of -3 with interpolated zeros . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 02 2008]
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FORMULA
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a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-3)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
a(n)=2*a(n-1)-4*a(n-2), a(0)=1, a(1)=1 . a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-3)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
a(n)=Sum_{k, 0<=k<=n}A124182(n,k)*(-4)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 15 2008]
a(n)=(1/2)*{[1-I*sqrt(3)]^n+[1+I*sqrt(3)]^n}, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 18 2008]
a(n)=2^n*cos(pi*n/3) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 19 2008]
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CROSSREFS
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Cf. A104537, A128018.
Sequence in context: A092280 A070987 A079458 this_sequence A128018 A104537 A019240
Adjacent sequences: A138227 A138228 A138229 this_sequence A138231 A138232 A138233
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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 06 2008
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