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A290987
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Expansion of (1 - 2*x + x^2 - x^4 + x^3 + x^5)/((1 - x)^2*(1 - 2*x + x^3 - x^4)).
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3
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1, 2, 4, 8, 16, 32, 63, 122, 233, 441, 830, 1557, 2915, 5451, 10186, 19026, 35529, 66337, 123849, 231211, 431631, 805768, 1504193, 2807986, 5241856, 9785309, 18266848, 34099850, 63656272, 118831031, 221829087, 414101780, 773028830, 1443059634, 2693846606
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OFFSET
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0,2
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LINKS
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FORMULA
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MAPLE
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f:= gfun:-rectoproc({a(n)-3*a(n+1)+3*a(n+2)+a(n+3)-5*a(n+4)+4*a(n+5)-a(n+6), a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8, a(4) = 16, a(5) = 32}, a(n), remember):
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MATHEMATICA
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DeleteCases[#, 0] &@ CoefficientList[Series[(1-2x+x^2-x^4+x^3+x^5)/((1-x)^2*(1-2x +x^3-x^4)), {x, 0, 34}], x] (* Michael De Vlieger, Aug 16 2017 *)
LinearRecurrence[{4, -5, 1, 3, -3, 1}, {1, 2, 4, 8, 16, 32}, 40] (* Vincenzo Librandi, Aug 17 2017 *)
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PROG
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(Magma) I:=[1, 2, 4, 8, 16, 32]; [n le 6 select I[n] else 4*Self(n-1)-5*Self(n-2) +Self(n-3)+3*Self(n-4)-3*Self(n-5)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Aug 17 2017
(PARI) Vec((1-2*x+x^2-x^4+x^3+x^5)/((1-x)^2*(1-2*x+x^3-x^4)) + O(x^50)) \\ Michel Marcus, Aug 17 2017
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-2*x+x^2-x^4+x^3+x^5)/((1-x)^2*(1-2*x+x^3-x^4)) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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