LucasL

LucasL(n)

gives the nth Lucas number.

LucasL(n, var)

returns the nth Lucas polynomial for variable var.

Lucas numbers satisfy a recurrence relation similar to that of the Fibonacci sequence, in which each term is the sum of the preceding two. They are generated by choosing the initial values LucasL(0) = 2 and LucasL(1) = 1.

See

• Wikipedia - Lucas number
• Wikipedia - Fibonacci polynomials

Examples

>> LucasL(10)
123

>> LucasL(50, x)
2+625*x^2+32500*x^4+672750*x^6+7400250*x^8+50075025*x^10+227613750*x^12+
736618125*x^14+1767883500*x^16+3241119750*x^18+4639918800*x^20+5272635000*x^22+
4814145000*x^24+3562467300*x^26+2148789800*x^28+1059575660*x^30+427248250*x^32+
140512125*x^34+37469900*x^36+8021650*x^38+1357510*x^40+177375*x^42+17250*x^44+
1175*x^46+50*x^48+x^50

Implementation status

• ☑ - partially implemented

Github

• Implementation of LucasL