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A227360
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G.f.: 1/(1 - x*(1-x^3)/(1 - x^2*(1-x^4)/(1 - x^3*(1-x^5)/(1 - x^4*(1-x^6)/(1 - ...))))), a continued fraction.
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7
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1, 1, 1, 2, 2, 3, 5, 6, 10, 14, 21, 32, 46, 71, 104, 157, 235, 350, 527, 785, 1179, 1763, 2639, 3954, 5915, 8861, 13262, 19857, 29731, 44507, 66640, 99765, 149366, 223625, 334795, 501247, 750434, 1123518, 1682076, 2518314, 3770306, 5644701, 8450977, 12652376
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OFFSET
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0,4
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COMMENTS
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Compare to the continued fraction representation for the g.f. of A173173, where A173173(n) = ceiling(Fibonacci(n)/2).
Limit a(n)/a(n+1) = 0.6679357039724580760720733281356826861233293827578332775311...
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 10*x^8 +...
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MATHEMATICA
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nMax = 44; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x] &; A227360 = col[2][[1 ;; nMax]] (* Jean-François Alcover, Nov 03 2016 *)
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PROG
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(PARI) {a(n)=local(CF); CF=1+x; for(k=0, n, CF=1/(1 - x^(n-k+1)*(1 - x^(n-k+3))*CF+x*O(x^n))); polcoeff(CF, n)}
for(n=0, 50, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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