Lucas sequence

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Lucas sequence

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In mathematics, the Lucas sequences and are certain constant-recursive integer sequences that satisfy the recurrence relation where and are fixed integers. Any sequence satisfying this recurrence relation can be represented as a linear combination of the Lucas sequences and . More generally, Lucas sequences and represent sequences of polynomials in and with integer coefficients. Famous examples of Lucas sequences include the Fibonacci numbers, Mersenne numbers, Pell numbers, Lucas numbers, Jacobsthal numbers, and a superset of Fermat numbers. Lucas sequences are named after the French mathematician Édouard Lucas.

English Wikipedia http://en.wikipedia.org/wiki/Lucas_sequence

Spanish wikipedia http://es.wikipedia.org/wiki/Sucesión_de_Lucas

Wiki page external link http://www.fq.math.ca/Scanned/39-5/yabuta.pdf http://www.joye.site88.net/papers/JQ96lucas.pdf http://www.fq.math.ca/Scanned/18-4/somer.pdf https://www.encyclopediaofmath.org/index.php/Lucas_sequence