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A295334
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Denominators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1.
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3
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1, 1, 2, 5, 7, 12, 31, 43, 74, 191, 265, 456, 1177, 1633, 2810, 7253, 10063, 17316, 44695, 62011, 106706, 275423, 382129, 657552, 1697233, 2354785, 4052018, 10458821, 14510839, 24969660, 64450159, 89419819, 153869978, 397159775, 551029753, 948189528, 2447408809, 3395598337, 5843007146
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OFFSET
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0,3
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COMMENTS
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The numerators are given in A295333. There details are given.
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LINKS
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FORMULA
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G.f.: G(x) = (1 + x + 2*x^2 - x^3 + x^4)/(1 - 6*x^3 - x^6), For the derivation see A295333, but here the input of the recurrence is a(0) = 1, a(-1) = 0 (a(-2) = a(0) = 1). This leads here to G_0 = 1+ 2*x*G_2 + x*G_1, G_1 = G_0 + x*G_2, G_2 = G_1 + G_0 and the solution gives G(x).
a(n) = 6*a(n-3) + a(n-6), n >= 6, with inputs a(0)..a(5).
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EXAMPLE
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For the first convergents see A295333.
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MAPLE
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numtheory:-cfrac(sqrt(5/2), 100, 'con'):
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,frac,cofr,easy
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AUTHOR
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STATUS
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approved
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