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A041006
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Numerators of continued fraction convergents to sqrt(6).
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15
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2, 5, 22, 49, 218, 485, 2158, 4801, 21362, 47525, 211462, 470449, 2093258, 4656965, 20721118, 46099201, 205117922, 456335045, 2030458102, 4517251249, 20099463098, 44716177445, 198964172878, 442644523201, 1969542265682, 4381729054565, 19496458483942
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: (2 + 5*x + 2*x^2 - x^3)/(1 - 10*x^2 + x^4).
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MATHEMATICA
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LinearRecurrence[{0, 10, 0, -1}, {2, 5, 22, 49}, 50] (* Vincenzo Librandi, Jun 10 2015 *)
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PROG
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(Magma) I:=[2, 5, 22, 49]; [n le 4 select I[n] else 10*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 10 2015
(PARI) A41006=contfracpnqn(c=contfrac(sqrt(6)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n)=A41006[n+1]! For correct index & more terms:
extend(A, c, N)={for(n=#A+1, #A=Vec(A, N), A[n]=[A[n-i]|i<-c[, 1]]*c[, 2]); A} \\ (End)
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CROSSREFS
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KEYWORD
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nonn,cofr,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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