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A057597
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a(n)=-a(n-1)-a(n-2)+a(n-3), a(0)=0,a(1)=0,a(2)=1.
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7
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0, 0, 1, -1, 0, 2, -3, 1, 4, -8, 5, 7, -20, 18, 9, -47, 56, 0, -103, 159, -56, -206, 421, -271, -356, 1048, -963, -441, 2452, -2974, 81, 5345, -8400, 3136, 10609, -22145, 14672, 18082, -54899, 51489, 21492, -127880, 157877, -8505, -277252, 443634, -174887, -545999, 1164520, -793408, -917111
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Reflected (A074058) tribonacci numbers A000073: A000073(n) = a(1-n).
There is an alternative way to produce this sequence, from A000073, which is 0,0,1,1,2,4,7,13,24,44,... Call this {b(n)}. Taking x1 = (b(2))^2 - b(1)*b(3) = 0; x2 = (b(3))^2 - b(2)*b(4) = 1; x3 = (b(4))^2 - b(3)*b(5) = -1; x4 = 0, x5 = 2, we generate (0),0,1,-1,0,2,-3,1. - John McNamara (mistermac39(AT)yahoo.com), Jan 02 2004
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REFERENCES
| Petho Attila, Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Oct 06 2000.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,-1,1).
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FORMULA
| G.f.: x^2/(1+x+x^2-x^3).
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MATHEMATICA
| CoefficientList[Series[x^2/(1+x+x^2-x^3), {x, 0, 50}], x]
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PROG
| (PARI) {a(n) = polcoeff( if( n<0, x / ( 1 - x - x^2 - x^3), x^2 / ( 1 + x + x^2 - x^3) ) + x*O(x^abs(n)), abs(n))} /* Michael Somos Sep 03 2007 */
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CROSSREFS
| Cf. A000073.
Sequence in context: A118800 A200139 A075297 * A121340 A165241 A119865
Adjacent sequences: A057594 A057595 A057596 * A057598 A057599 A057600
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 06 2000
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