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A027943
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a(n) = T(2*n+1, n+3), T given by A027935.
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1
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1, 22, 155, 709, 2587, 8273, 24416, 68595, 187030, 500950, 1327986, 3499982, 9195035, 24115804, 63192397, 165512723, 433410661, 1134800215, 2971089810, 7778591025, 20364830496, 53316076892, 139583609940, 365435000524, 956721681957, 2504730383698, 6557469861231
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OFFSET
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2,2
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LINKS
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FORMULA
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G.f.: x^2*(1+14*x+5*x^2-4*x^3) / ((1-x)^5*(1-3*x+x^2)). - Colin Barker, Feb 20 2016
a(n) = Sum_{j=0..n-2} binomial(2*n-j+1, 2*(n-j-2)).
a(n) = Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6. (End)
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MAPLE
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with(combinat); seq(fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6, n=2..40); # G. C. Greubel, Sep 28 2019
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MATHEMATICA
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Table[Fibonacci[2*n+7] - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6, {n, 2, 40}]
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PROG
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(PARI) vector(30, n, my(m=n+1); fibonacci(2*m+7) - (4*m^4 +12*m^3 +35*m^2 +75*m +78)/6) \\ G. C. Greubel, Sep 28 2019
(Magma) [Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6: n in [2..40]]; // G. C. Greubel, Sep 28 2019
(Sage) [fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6 for n in (2..40)] # G. C. Greubel, Sep 28 2019
(GAP) List([2..40], n-> Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6 ); # G. C. Greubel, Sep 28 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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