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A295334 Denominators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The numerators are given in A295333. There details are given.

LINKS

Robert Israel, Table of n, a(n) for n = 0..3795

Index entries for linear recurrences with constant coefficients, signature (0, 0, 6, 0, 0, 1).

FORMULA

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).

EXAMPLE

For the first convergents see A295333.

MAPLE

numtheory:-cfrac(sqrt(5/2), 100, 'con'):

map(denom, con[1..-2]); # Robert Israel, Nov 22 2017

MATHEMATICA

Denominator[Convergents[Sqrt[5/2], 50]] (* Wesley Ivan Hurt, Nov 21 2017 *)

CROSSREFS

Cf. A020797, A295333.

Sequence in context: A230428 A071013 A114727 * A041033 A134472 A041203

Adjacent sequences:  A295331 A295332 A295333 * A295335 A295336 A295337

KEYWORD

nonn,frac,cofr,easy

AUTHOR

Wolfdieter Lang, Nov 21 2017

STATUS

approved

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Last modified May 21 06:36 EDT 2022. Contains 353889 sequences. (Running on oeis4.)