A370179 a(n) = floor(x*a(n-1)) for n > 0 where x = (9 + 3*sqrt(13))/2, a(0) = 1.

1, 9, 89, 881, 8729, 86489, 856961, 8491049, 84132089, 833608241, 8259662969, 81839440889, 810891934721, 8034582380489, 79609268836889, 788794660956401, 7815635368139609, 77439870261864089, 767299550670033281, 7602654788387076329, 75329589051513986489

Offset: 0

Author

Philippe Deléham, Apr 24 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,0,-9).

Crossrefs

Cf. A057092, A090655 (x value), A370174.

Programs

Mathematica

LinearRecurrence[{10,0,-9},{1,9,89},21] (* Stefano Spezia, Apr 24 2024 *)

Formula

a(n) = 10*a(n-1) - 9*a(n-3) for n > 2, a(0) = 1, a(1) = 9, a(2) = 89.

a(n) = 9*a(n-1) + 9*a(n-2) - 1.

G.f.: (1-x-x^2)/((1-x)*(1-9*x-9*x^2)).

a(n) = Sum_{k = 0..n} A370174(n,k)*8^k.

a(n) = (16*A057092(n) + 8*A057092(n-1) + 1)/17.