A295332 Denominators of the continued fraction convergents to sqrt(13)/2 = A295330.

1, 1, 5, 71, 289, 360, 1009, 1369, 6485, 92159, 375121, 467280, 1309681, 1776961, 8417525, 119622311, 486906769, 606529080, 1699964929, 2306494009, 10925940965, 155269667519, 632004611041, 787274278560, 2206553168161, 2993827446721, 14181862955045, 201539908817351, 820341498224449, 1021881407041800, 2864104312308049, 3885985719349849, 18408047189707445

Offset

0,3

Comments

The numerators are given in A295331.

The continued fraction expansion of sqrt(13)/2 is [1, repeat(1, 4, 14, 4, 1, 2)].

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1298, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (1 + x + 5*x^2 + 71*x^3 + 289*x^4 + 360*x^5 - 289*x^6 + 71*x^7 - 5*x^8 + x^9 - x^10) / ((1 - 3*x - x^2)*(1 + 3*x - x^2)*(1 + 3*x + 10*x^2 - 3*x^3 + x^4)*(1 - 3*x + 10*x^2 + 3*x^3 + x^4)). See A295331 for a hint for the derivation. Here the a(n) recurrence is the same as there but the inputs are a(0) = 1, a(-1) = 0, (a(-2) = 1). The unfactorized denominator is 1 - 1298*x^6 + x^12.

a(n) = 1298*a(n-6) - a(n-12), n >= 12, with inputs a(0)..a(11).

Example

See A295331 for the first convergents.

Crossrefs

Cf. A295330, A295331.

Sequence in context: A142052 A139930 A265030 * A123077 A171554 A197405

Adjacent sequences: A295329 A295330 A295331 * A295333 A295334 A295335

Keyword

nonn,frac,cofr,easy

Author

Wolfdieter Lang, Nov 20 2017

Status

approved