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A138230
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Expansion of (1-x)/(1-2x+4x^2).
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| 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 (paoloplava(AT)gmail.com), Nov 18 2008]
a(n)=2^n*cos(pi*n/3) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 19 2008]
a(n) = -8 * a(n-3). - Paul Curtz, Apr 22 2011
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CROSSREFS
| Cf. A104537, A128018. A088138.
Sequence in context: A070987 A168286 A079458 * A128018 A104537 A019240
Adjacent sequences: A138227 A138228 A138229 * A138231 A138232 A138233
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 06 2008
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