A341927 Bisection of the numerators of the convergents of cf(1,4,1,6,1,6,...,6,1).

1, 6, 47, 370, 2913, 22934, 180559, 1421538, 11191745, 88112422, 693707631, 5461548626, 42998681377, 338527902390, 2665224537743, 20983268399554, 165200922658689, 1300624112869958, 10239791980300975, 80617711729537842, 634701901856001761, 4996997503118476246, 39341278123091808207

Offset

0,2

Comments

15*a(n)^2 - 11 is a square for all terms.

x = a(n) and y = a(n+1) satisfy x^2 + y^2 - 8*x*y = -11.

x = a(n) and y = a(n+2) satisfy x^2 + y^2 - 62*x*y = -704.

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (8,-1).

Formula

a(0) = 1; a(1) = 6; a(n) = 8*a(n-1) - a(n-2).

G.f.: (1 - 2*x)/(1 - 8*x + x^2). - Stefano Spezia, Feb 26 2021

a(n) = A237262(2*n + 1).

Example

a(3) = 8*6 - 1 = 47.

Mathematica

LinearRecurrence[{8, -1}, {1, 6}, 15]

Prog

(PARI) my(p=Mod('x, 'x^2-8*'x+1)); a(n) = subst(lift(p^n), 'x, 6); \\ Kevin Ryde, Mar 01 2021

Crossrefs

Bisection of A237262.

Cf. A341929.

Sequence in context: A024076 A015553 A291028 * A071878 A369502 A364748

Adjacent sequences: A341924 A341925 A341926 * A341928 A341929 A341930

Keyword

nonn,easy

Author

John O. Oladokun, Feb 23 2021

Status

approved