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A341927 Bisection of the numerators of the convergents of cf(1,4,1,6,1,6,...,6,1). 1
1, 6, 47, 370, 2913, 22934, 180559, 1421538, 11191745, 88112422, 693707631, 5461548626, 42998681377, 338527902390, 2665224537743, 20983268399554, 165200922658689, 1300624112869958, 10239791980300975, 80617711729537842, 634701901856001761, 4996997503118476246, 39341278123091808207 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
John O. Oladokun, Feb 23 2021
STATUS
approved

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Last modified July 18 13:57 EDT 2024. Contains 374378 sequences. (Running on oeis4.)