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
Examples
a(3) = 8*6 - 1 = 47.
Links
- Index entries for linear recurrences with constant coefficients, signature (8,-1).
Programs
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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).
Comments