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A117575
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Expansion of (1-x^3)/((1-x)*(1+2*x^2)).
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2
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1, 1, -1, -2, 2, 4, -4, -8, 8, 16, -16, -32, 32, 64, -64, -128, 128, 256, -256, -512, 512, 1024, -1024, -2048, 2048, 4096, -4096, -8192, 8192, 16384, -16384, -32768, 32768, 65536, -65536, -131072, 131072, 262144, -262144, -524288, 524288
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums of A116949.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,-2).
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FORMULA
| a(n) = a(n-1)-2*a(n-2)+2*a(n-3), n>=3;
a(n) = (cos(pi*/2)+sin(pi*n/2)) * (2^((n-1)/2)*(1-(-1)^n)/2 + 2^((n-2)/2)*(1+(-1)^n)/2 + 0^n/2).
a(n+1) = Sum_{k, 0<=k<=n} A122016(n,k)*(-1)^k. - DELEHAM Philippe, Jan 31 2012
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PROG
| (PARI) a(n)=if(n, (-1)^(n\2)<<((n-1)\2), 1) \\ Charles R Greathouse IV, Jan 31 2012
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CROSSREFS
| Cf. A016116.
Sequence in context: A082267 A076939 A158780 * A131572 A152166 A016116
Adjacent sequences: A117572 A117573 A117574 * A117576 A117577 A117578
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 29 2006
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