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A041008
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Numerators of continued fraction convergents to sqrt(7).
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11
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2, 3, 5, 8, 37, 45, 82, 127, 590, 717, 1307, 2024, 9403, 11427, 20830, 32257, 149858, 182115, 331973, 514088, 2388325, 2902413, 5290738, 8193151, 38063342, 46256493, 84319835, 130576328, 606625147, 737201475, 1343826622, 2081028097, 9667939010, 11748967107, 21416906117
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (2 + 3*x + 5*x^2 + 8*x^3 + 5*x^4 - 3*x^5 + 2*x^6 - x^7)/(1 - 16*x^4 + x^8).
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 16, 0, 0, 0, -1}, {2, 3, 5, 8, 37, 45, 82, 127}, 40] (* Harvey P. Dale, Jul 23 2021 *)
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PROG
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(PARI) A041008=contfracpnqn(c=contfrac(sqrt(7)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n)=A041008[n+1]! For more terms use:
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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Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041010 (m=8), A005667 (m=10), A041014 (m=11), A041016 (m=12), ..., A042934 (m=999), A042936 (m=1000).
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KEYWORD
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nonn,cofr,frac,easy
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AUTHOR
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STATUS
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approved
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