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A105371
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Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4).
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7
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1, 1, 1, 0, -3, -8, -13, -13, 0, 34, 89, 144, 144, 0, -377, -987, -1597, -1597, 0, 4181, 10946, 17711, 17711, 0, -46368, -121393, -196418, -196418, 0, 514229, 1346269, 2178309, 2178309, 0, -5702887, -14930352, -24157817, -24157817, 0, 63245986, 165580141
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Binomial transform of A105367.
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LINKS
| Index entries for two-way infinite sequences
Index to sequences with linear recurrences with constant coefficients, signature (3,-4,2,-1)
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FORMULA
| G.f. : (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4); a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4); (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*pi*n/5))
a(5n)=-F(-5n-1), a(5n+1)=a(5n+2)=-F(-5n-2), a(5n+3)=0, a(5n+4)=F(-5n-4). - Michael Somos Apr 9 2005
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PROG
| (PARI) a(n)=local(m); m=n%5+1; [1, -1, -1, 0, 1][m]*fibonacci(-n-(m<3)) /* Michael Somos Apr 9 2005 */
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CROSSREFS
| Cf. A000045.
Sequence in context: A032046 A180507 A131213 * A038188 A043361 A023734
Adjacent sequences: A105368 A105369 A105370 * A105372 A105373 A105374
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
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