The Jacobsthal sequence is an additive sequence similar to the Fibonacci sequence, defined by the recurrence relation Jn = Jn-1 + Jn-2, with initial terms J0 = 0 and J1 = 1. A number in the sequence is called a Jacobsthal number. They are a specific type of Lucas sequence Un(P, Q) for which P = -1 and Q = -2.
0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, ……
Jacobsthal numbers are defined by the recurrence relation:
J(n) = 0 if n == 0
J(n) = 1 if n == 1
J(n) = J(n-1) + 2*J(n-2) otherwise
Jacobsthal-Lucas numbers Jacobsthal-Lucas numbers represent the complementary Lucas sequence Vn(1, -2). They satisfy the same recurrence relation as Jacobsthal numbers but have different initial values:
L(n) = 0 if n == 0
L(n) = 1 if n == 1
L(n) = L(n-1) + 2*L(n-2) otherwise
Input : n = 5
Output :
Jacobsthal number: 11
Jacobsthal-Lucas number: 31
Input : n = 4
Output :
Jacobsthal number: 5
Jacobsthal-Lucas number: 17