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A294972
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Numerators of continued fraction convergents to sqrt(7)/2.
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4
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1, 4, 41, 127, 295, 1012, 10415, 32257, 74929, 257044, 2645369, 8193151, 19031671, 65288164, 671913311, 2081028097, 4833969505, 16582936612, 170663335625, 528572943487, 1227809222599, 4212000611284, 43347815335439, 134255446617601, 311858708570641, 1069831572329524, 11010174431865881
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OFFSET
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0,2
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COMMENTS
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The denominators are given in A294973.
The continued fraction expansion of sqrt(7)/2 is 1, repeat(3, 10, 3, 2).
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LINKS
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FORMULA
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G.f.: (1 + 4*x + 41*x^2 + 127*x^3 + 41*x^4 - 4*x^5 + x^6 - x^7) / ((1 - 16*x^2 + x^4)*(1 + 16*x^2 + x^4)).
a(n) = 254*a(n-4) - a(n-8) for n > 7.
(End)
The proof of the g.f. runs like the one given for the denominators in A294973. The recurrence for a(n) is the same but the input is now a(0) = b(0) = 1 and a(-1) = 1, (a(-2) = 0). - Wolfdieter Lang, Nov 19 2017
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MATHEMATICA
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PROG
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(PARI) Vec((1 + 4*x + 41*x^2 + 127*x^3 + 41*x^4 - 4*x^5 + x^6 - x^7) / ((1 - 16*x^2 + x^4)*(1 + 16*x^2 + x^4)) + O(x^40)) \\ Colin Barker, Nov 21 2017
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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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STATUS
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approved
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