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A133585
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Expansion of x - x^2*(2*x+1)*(x^2-2) / ( (x^2-x-1)*(x^2+x-1) ).
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3
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1, 2, 4, 5, 10, 13, 26, 34, 68, 89, 178, 233, 466, 610, 1220, 1597, 3194, 4181, 8362, 10946, 21892, 28657, 57314, 75025, 150050, 196418, 392836, 514229, 1028458, 1346269, 2692538, 3524578, 7049156, 9227465, 18454930, 24157817
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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For even-indexed terms, a(n) = F(n+1). For odd-indexed terms (n>1), a(n) = 2*a(n-1), A126358.
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EXAMPLE
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a(4) = F(5) = 5.
a(5) = 2*a(4) = 2*5 = 10.
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MAPLE
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A133585aux := proc(n, k)
end proc:
combinat[fibonacci](n) ;
end proc:
add(A133585aux(n, j)*A000045(j), j=0..n) ;
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MATHEMATICA
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CoefficientList[Series[1 - x (2 x + 1) (x^2 - 2)/((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 21 2015 *)
LinearRecurrence[{0, 3, 0, -1}, {1, 2, 4, 5, 10}, 40] (* Harvey P. Dale, Mar 04 2019 *)
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PROG
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(PARI) a(n)=if(n>1, ([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 3, 0]^(n-2)*[2; 4; 5; 10])[1, 1], 1) \\ Charles R Greathouse IV, Jun 20 2015
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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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EXTENSIONS
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Previous name corrected and new name from R. J. Mathar, Jun 20 2015
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STATUS
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approved
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