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A136161
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a(n) = 2*a(n-3)-a(n-6), starting a(0..5) = 0, 5, 2, 1, 3, 1.
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0
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0, 5, 2, 1, 3, 1, 2, 1, 0, 3, -1, -1, 4, -3, -2, 5, -5, -3, 6, -7, -4, 7, -9, -5, 8, -11, -6, 9, -13, -7, 10, -15, -8, 11, -17, -9, 12, -19, -10, 13, -21, -11, 14, -23, -12, 15, -25, -13, 16, -27, -14
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The intent is to show the triples (0,5,2), (1,3,1), (2,1,0), etc of the coefficients (k,5-2k,2-k), k=0,1,2,... that define recurrences a(n) = k*a(n-1) + (5-2k)*a(n-2) + (2-k)*a(n-3).
The first triple describes linear recurrences with "signature" 0, 5, 2 like A112685, A135138 etc.
The second triple describes linear recurrences with "signature" 1, 3, 1 like A097076. (See the OEIS index "recurrence, linear.." for more examples.)
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,2,0,0,-1)
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FORMULA
| G.f. -x*(-5-2*x-x^2+7*x^3+3*x^4) / ( (x-1)^2*(1+x+x^2)^2 ). - R. J. Mathar, Jul 06 2011
a(3n) = n. a(3n+1) = 5-2n. a(3n+3)=2-n.
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PROG
| (PARI) Vec(-x*(-5-2*x-x^2+7*x^3+3*x^4) / ( (x-1)^2*(1+x+x^2)^2+O(x^99)) \\ Charles R Greathouse IV, Jul 06 2011
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CROSSREFS
| Cf. A135997, A137241.
Sequence in context: A038631 A158625 A133615 * A197383 A091505 A030357
Adjacent sequences: A136158 A136159 A136160 * A136162 A136163 A136164
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KEYWORD
| sign,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Mar 16 2008
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