README
¶
lucas
Go package to generate and count Nth number of Lucas sequence (Fibonacci, Lucas, Pell, etc.s). Nth counting is optimized
This library supports big numbers and return big.Int pointer(s).
Example
fib9 := lucas.GenerateFibonacci(10)
fmt.Println(fib9[9].Int64()) // 34
fib10 := lucas.NthFibonacci(10)
fmt.Println(fib10.Int64()) // 55
Installation
go get github.com/hamonangann/lucas
Contribution
Fork this repository, then open a pull request to improve this project. I welcome any kind of contributions!
If you have any questions, please raise an issue.
Documentation
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Overview ¶
Package lucas is a library for generating Lucas sequence and counting Nth number of Lucas sequence. There are many sequences supported (see example.go)
- Fibonacci numbers - Lucas numbers - Pell numbers - Counting numbers - Jacobsthal numbers - Generalized Lucas sequences by setting two (P and Q) parameters
This library supports big numbers and return big.Int pointer(s)
Example:
fib9 := lucas.GenerateFibonacci(10) fmt.Println(fib9[9].Int64()) // 34 fib10 := lucas.NthFibonacci(10) fmt.Println(fib10.Int64()) // 55
Index ¶
- func GenerateCounting(n uint) []*big.Int
- func GenerateFibonacci(n uint) []*big.Int
- func GenerateJacobsthal(n uint) []*big.Int
- func GenerateJacobsthalLucas(n uint) []*big.Int
- func GenerateLucas(n uint) []*big.Int
- func GeneratePell(n uint) []*big.Int
- func GeneratePellLucas(n uint) []*big.Int
- func GenerateSequenceU(p int64, q int64, n uint) []*big.Int
- func GenerateSequenceV(p int64, q int64, n uint) []*big.Int
- func NthCounting(n uint) *big.Int
- func NthFibonacci(n uint) *big.Int
- func NthJacobsthal(n uint) *big.Int
- func NthJacobsthalLucas(n uint) *big.Int
- func NthLucas(n uint) *big.Int
- func NthPell(n uint) *big.Int
- func NthPellLucas(n uint) *big.Int
- func NthSequenceU(p int64, q int64, n uint) *big.Int
- func NthSequenceV(p int64, q int64, n uint) *big.Int
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func GenerateCounting ¶
GenerateCounting returns first n counting numbers (0 to n-1) e.g. [0 1 2 3 4 5 6 7 8 9 10]
func GenerateFibonacci ¶
GenerateFibonacci returns first n Fibonacci numbers (F[0] to F[n-1]) e.g. [0 1 1 2 3 5 8 13 21 34 55]
func GenerateJacobsthal ¶
GenerateJacobsthal returns first n Jacobsthal numbers (J[0] to J[n-1]) e.g. [0 1 1 3 5 11 21 43 85 171 341]
func GenerateJacobsthalLucas ¶
GenerateJacobsthalLucas returns first n Jacobsthal-Lucas (companion Jacobsthal) numbers (j[0] to j[n-1]) e.g. [2 1 5 7 17 31 65 127 257 511 1025]
func GenerateLucas ¶
GenerateLucas returns first n Lucas numbers (L[0] to L[n-1]) e.g. [2 1 3 4 7 11 18 29 47 76 123]
func GeneratePell ¶
GeneratePell returns first n Pell numbers (P[0] to P[n-1]) e.g. [0 1 2 5 12 29 70 169 408 985 2378]
func GeneratePellLucas ¶
GeneratePellLucas returns first n Pell-Lucas (companion Pell) numbers (Q[0] to Q[n-1]) e.g. [2 2 6 14 34 82 198 478 1154 2786 6726]
func GenerateSequenceU ¶
GenerateSequenceU returns first n numbers of first kind of Lucas Sequence (U[0] to U[n-1]) Choose this sequence to get starting U[0] = 0, U[1] = 1 Choose P, Q so that U[n] = P*U[n-1] - Q*U[n-2] Complexity: O(n)
func GenerateSequenceV ¶
GenerateSequenceV returns first n numbers of second kind of Lucas Sequence (V[0] to V[n-1]) Choose this sequence to get starting V[0] = 2, V[1] = P Choose P, Q so that V[n] = P*V[n-1] - Q*V[n-2] Complexity: O(n)
func NthCounting ¶
NthCounting returns n-th counting number (zero-indexed) e.g. N[10] = 10
func NthFibonacci ¶
NthFibonacci returns n-th Fibonacci number (zero-indexed) e.g. F[10] = 55
func NthJacobsthal ¶
NthJacobsthal returns n-th Jacobsthal number (zero-indexed) e.g. J[10] = 341
func NthJacobsthalLucas ¶
NthJacobsthalLucas returns n-th Jacobsthal-Lucas (companion Jacobsthal) number (zero-indexed) e.g. j[10] = 1025
func NthPellLucas ¶
NthPellLucas returns n-th Pell-Lucas (companion Pell) number (zero-indexed) e.g. Q[10] = 6726
func NthSequenceU ¶
NthSequenceU returns n-th number of first kind of Lucas Sequence (zero-indexed) It is optimized with fast-doubling and thread-safe memoization to support larger n numbers Choose this sequence to get starting U[0] = 2, U[1] = P Choose P, Q so that U[n] = P*U[n-1] - Q*U[n-2] Complexity: O(log n)
func NthSequenceV ¶
NthSequenceV returns n-th number of second kind of Lucas Sequence (zero-indexed) It is optimized with fast-doubling, bin-exp, and thread-safe memoization to support larger n numbers Choose this sequence to get starting V[0] = 2, V[1] = P Choose P, Q so that V[n] = P*V[n-1] - Q*V[n-2] Complexity: O(log n)
Types ¶
This section is empty.
Source Files