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Recursive Sequences
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Flashcards
0/10
Geometric Progression
G(n) = G(n-1) * r with base case G(1) = a
Fibonacci Sequence
F(n) = F(n - 1) + F(n - 2) with base cases F(0) = 0 and F(1) = 1
Bell Numbers
B(n) = \sum_{k=0}^{n-1} \binom{n-1}{k} B(k) with base case B(0) = 1
Padovan Sequence
P(n) = P(n-2) + P(n-3) with base cases P(0) = P(1) = P(2) = 1
Pell Numbers
P(n) = 2 * P(n-1) + P(n-2) with base cases P(0) = 0 and P(1) = 1
Catalan Numbers
C(n) = \frac{(2n)!}{(n+1)!n!} for n≥0 (recursive formula can be defined in terms of earlier values as well)
Harmonic Sequence
H(n) = 1/n with base case H(1) = 1
Arithmetic Progression
A(n) = A(n-1) + d with base case A(1) = a
Lucas Numbers
L(n) = L(n-1) + L(n-2) with base cases L(0) = 2 and L(1) = 1
Factorial
n! = n * (n-1)! with base case 0! = 1
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