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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 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

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