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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in {\it Python}.
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참고문헌 (10)
참고문헌 신청
Goksal Bilgici / 2014 / Two generalizations of Lucas sequence / Applied Mathematics and Computation 245:526~538
C. Cooper / 2010 / An identity for period k second order linear recurrence systems / Congr. Numer 200:95~106
Marcia Edson / 2009 / A New Generalization of Fibonacci Sequence & Extended Binet's Formula / Integers 9(6):639~654
Dan Laksov / 1965 / Linear recurring sequences over finite fields / MATHEMATICA SCANDINAVICA 16:181~196
JUN MA / 2011 / WHEN THUE-MORSE MEETS KOCH / Fractals 13(03):191~206
C. Cooper / 2010 / An identity for period k second order linear recurrence systems / Congr. Numer 200:95~106
Marcia Edson / 2009 / A New Generalization of Fibonacci Sequence & Extended Binet's Formula / Integers 9(6):639~654
Dan Laksov / 1965 / Linear recurring sequences over finite fields / MATHEMATICA SCANDINAVICA 16:181~196
JUN MA / 2011 / WHEN THUE-MORSE MEETS KOCH / Fractals 13(03):191~206
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