A295334 Denominators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1.

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

Offset: 0

Author

Wolfdieter Lang, Nov 21 2017

Keywords

• nonn
• frac
• cofr
• easy

Comments

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

Examples

			For the first convergents see A295333.
		

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).

Crossrefs

Cf. A020797, A295333.

Programs

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 *)

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).