Integer sequences | Recurrence relations

Lucas sequence

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. (Wikipedia).

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Powered by https://www.numerise.com/ C1 Sequences & Series (1)

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Related pages

Lucas pseudoprime | Fibonacci number | Fibonacci polynomials | Somer–Lucas pseudoprime | Fermat's little theorem | Lucas–Lehmer primality test | Polynomial | Jacobsthal number | Chebyshev polynomials | Modular exponentiation | Pell number | Carmichael's theorem | Discriminant | Mersenne number | Baillie–PSW primality test | On-Line Encyclopedia of Integer Sequences | Legendre symbol | Square triangular number | Lucas number | Mathematics | Recurrence relation | Divisibility sequence | Linear combination | Constant-recursive sequence | Integer sequence | Fermat number | Lucas–Lehmer–Riesel test | Repunit | Édouard Lucas | Exponentiation by squaring | Frobenius pseudoprime | Generating function