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A341929
Bisection of the numerators of the convergents of cf (1,1,6,1,6,1,...,6,1).
1
1, 2, 15, 118, 929, 7314, 57583, 453350, 3569217, 28100386, 221233871, 1741770582, 13712930785, 107961675698, 849980474799, 6691882122694, 52685076506753, 414788729931330, 3265624762943887, 25710209373619766, 202416050226014241, 1593618192434494162, 12546529489249939055, 98778617721565018278
OFFSET
0,2
COMMENTS
15*a(n)^2 - 11 is a square for all terms.
x = a(n) and y = a(n+1) satisfy the equation 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.
FORMULA
a(n) = 8*a(n-1) - a(n-2) for n >= 2.
a(n) = A237262(2*n) for n >= 1.
G.f.: (1 - 6*x)/(1 - 8*x + x^2). - Stefano Spezia, Mar 01 2021
EXAMPLE
a(3) = 8*15 - 2 = 118.
MATHEMATICA
LinearRecurrence [{8, -1}, {1, 2}, 15]
PROG
(PARI) my(p=Mod('x, 'x^2-8*'x+1)); a(n) = subst(lift(p^n), 'x, 2); \\ Kevin Ryde, Feb 27 2021
CROSSREFS
After a(0), bisection of A237262.
Cf. A341927.
Sequence in context: A161937 A369203 A074621 * A185758 A052448 A168502
KEYWORD
nonn,easy
AUTHOR
John O. Oladokun, Feb 23 2021
STATUS
approved