Lucas Numbers: Difference between revisions
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The Lucas numbers are closely related to the Fibonacci numbers, using the same recurrence relation but with different initial conditions. | The Lucas numbers are closely related to the Fibonacci numbers, using the same recurrence relation but with different initial conditions. | ||
<math> | |||
L(n) = L(n-1) + L(n-2) \qquad L(0) = 2, L(1) = 1 | |||
</math> | |||
Compare to the original Fibonacci sequence: | |||
<math> | |||
F(n) = F(n-1) + F(n-2) \qquad F(0) = 2, F(1) = 1 | |||
</math> | |||
Revision as of 22:54, 16 July 2017
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Mathematical Constants
Irrational Numbers: Euler-Mascheroni Constant · Sqrt2 · Phi · Sqrt3 · e · Sqrt5 · Sqrt6 · Sqrt7 · Sqrt8 · Pi · Sqrt10 · Sqrt11 · Pi to the Pi Prime Numbers: Prime Numbers · Palindromic Primes · Prime Generating Polynomials · Belphegors Prime Sequences: Fibonacci Numbers · Lucas Numbers · General Fibonacci Numbers Number Forms: Fermat Numbers · Mersenne Primes · Counting and Combinatorics: Catalan Numbers · Shannon Number · Eddington Number Tetration and Knuth's Up Notation: Tetration Factoring and Number Theory: Divisibility · Totient Function Games: Four Fours · Five Fives
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The Lucas numbers are closely related to the Fibonacci numbers, using the same recurrence relation but with different initial conditions.
$ L(n) = L(n-1) + L(n-2) \qquad L(0) = 2, L(1) = 1 $
Compare to the original Fibonacci sequence:
$ F(n) = F(n-1) + F(n-2) \qquad F(0) = 2, F(1) = 1 $