A162671 Generalized Fibonacci numbers

1, 1, 101, 102, 10301, 10403, 1050601, 1061004, 107151001, 108212005, 10928351501, 11036563506, 1114584702101, 1125621265607, 113676711262801, 114802332528408, 11593909964103601, 11708712296632009

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Index entries for linear recurrences with constant coefficients, signature (0,102,0,-1).

Formula

For n even a(n) = a(n-1) + a(n-2), for n odd a(n) = 100*a(n-1)+ a(n-2); with a(0) = 0, a(1) = 1

a(n)=102*a(n-2)-a(n-4). G.f.: -x*(-1-x+x^2)/((x^2+10*x-1)*(x^2-10*x-1)). [From R. J. Mathar, Jul 14 2009]

Mathematica

LinearRecurrence[{0, 102, 0, -1}, {1, 1, 101, 102}, 20] (* Harvey P. Dale, May 08 2020 *)

Crossrefs

Partly same as A041059 (and its palindromic partner-sequence A015446). A007318.

Sequence in context: A261021 A271642 A164849 * A230094 A030474 A162199

Adjacent sequences: A162668 A162669 A162670 * A162672 A162673 A162674

Keyword

nonn

Author

Mark Dols, Jul 10 2009

Extensions

More terms from R. J. Mathar, Jul 14 2009

Status

approved