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A104161
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G.f.: x*(1 - x + x^2)/((1-x)^2 * (1 - x - x^2)).
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16
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0, 1, 2, 5, 10, 19, 34, 59, 100, 167, 276, 453, 740, 1205, 1958, 3177, 5150, 8343, 13510, 21871, 35400, 57291, 92712, 150025, 242760, 392809, 635594, 1028429, 1664050, 2692507, 4356586, 7049123
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OFFSET
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0,3
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COMMENTS
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A floretion-generated sequence.
Floretion Algebra Multiplication Program, FAMP Code: 1vesrokseq[ (- .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e)('i + i' + 'ji' + 'ki' + e) ] RokType: Y[sqa.Findk()] = Y[sqa.Findk()] + p.
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LINKS
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FORMULA
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Superseeker results (incomplete): a(2) - 2a(n+1) + a(n) = A006355(n+1) (Number of binary vectors of length n containing no singletons); a(n+1) - a(n) = A001595(n) (2-ranks of difference sets constructed from Segre hyperovals); a(n) + n + 1 = A001595(n+1).
a(n) = 2*(Fibonacci(n+2) - 1) - n.
a(n) = Sum_{k=0..n} A101220(n-k, 0, k). (End)
a(n) = a(n-1) + a(n-2) + n-1.
a(n) = row sums of A117501, starting (1, 2, 5, 10, ...). (End)
a(n) = (Sum_{k=0..n} (n-k)*Fibonacci(k-1) + Fibonacci(k)) - n. - Ross La Haye, May 31 2006
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=5. - Harvey P. Dale, Sep 06 2012
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MATHEMATICA
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CoefficientList[Series[x*(1-x+x^2)/((1-x)^2*(1-x-x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, -2, -1, 1}, {0, 1, 2, 5}, 40] (* Harvey P. Dale, Sep 06 2012 *)
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PROG
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(PARI) my(x='x+O('x^40)); concat(0, Vec(x*(1-x+x^2)/((1-x)^2*(1-x-x^2)))) \\ G. C. Greubel, Sep 26 2017
(Magma) [2*Fibonacci(n+2) -(n+2): n in [0..40]]; // G. C. Greubel, Jul 09 2019
(SageMath) [2*fibonacci(n+2) -(n+2) for n in (0..40)] # G. C. Greubel, Jul 09 2019
(GAP) List([0..40], n-> 2*Fibonacci(n+2) -(n+2)); # G. C. Greubel, Jul 09 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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