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

Author

John O. Oladokun, Feb 23 2021

Keywords

• nonn
• easy

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.

Examples

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

Links

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

Crossrefs

Bisection of A237262.

Cf. A341929.

Programs

Mathematica

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

PARI

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

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).