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A073028
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a(n) = max{ C(n,0), C(n-1,1), C(n-2,2), ..., C(n-n,n) }.
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6
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1, 1, 1, 2, 3, 4, 6, 10, 15, 21, 35, 56, 84, 126, 210, 330, 495, 792, 1287, 2002, 3003, 5005, 8008, 12376, 19448, 31824, 50388, 77520, 125970, 203490, 319770, 497420, 817190, 1307504, 2042975, 3268760, 5311735, 8436285, 13123110, 21474180, 34597290
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OFFSET
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0,4
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COMMENTS
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lim a(n)/a(n-1) = (1+sqrt(5))/2.
a(n-1) is the max coefficient in n-th Fibonacci polynomial (the polynomial F_0(x) is constant zero, and is not included in this sequence). - Vladimir Reshetnikov, Oct 09 2016
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REFERENCES
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Peter Boros (borospet(AT)freemail.hu): Lectures on Fibonacci's World at the SOTERIA Foundation, 1999.
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LINKS
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FORMULA
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a(n) ~ 5^(1/4) * phi^(n+1) / sqrt(2*Pi*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 09 2016
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EXAMPLE
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For n = 6, C(6,0) = 1, C(5,1) = 5, C(4,2) = 6, C(3,3) = 1. These binomial coefficients are the coefficients in the Fibonacci polynomial F_7(x) = x^6 + 5*x^4 + 6*x^2 + 1. The max coefficient is 6, so a(6) = 6.
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MATHEMATICA
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Table[Max[CoefficientList[Fibonacci[n + 1, x], x]], {n, 1, 30}] (* Vladimir Reshetnikov, Oct 07 2016 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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