The Jacobsthal polynomials are the w-polynomials obtained by setting p(x) = 1 and q(x) = 2x in the Lucas polynomial sequence. The first few Jacobsthal-Lucas polynomials are j_1(x) | = | 1 j_2(x) | = | 4x + 1 j_3(x) | = | 6x + 1 j_4(x) | = | 8x^2 + 8x + 1 j_5(x) | = | 20x^2 + 10x + 1. When evaluated at x = 1, the polynomials give the Jacobsthal-Lucas numbers j_n(1) = j_n.

Jacobsthal polynomial | Lucas polynomial sequence