Jacobsthal-Lucas number

The Jacobsthal numbers are the numbers obtained by the U_ns in the Lucas sequence with P = 1 and Q = - 2, corresponding to a = 2 and b = - 1. They and the Jacobsthal-Lucas numbers (the V_ns) satisfy the recurrence relation J_n = J_(n - 1) + 2J_(n - 2). The Jacobsthal numbers satisfy J_0 = 0 and J_1 = 1 and are 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ... (OEIS A001045). The Jacobsthal-Lucas numbers satisfy j_0 = 2 and j_1 = 1 and are 2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, ... (OEIS A014551). The properties of these numbers are summarized in Horadam.

Jacobsthal-Lucas polynomial | Jacobsthal polynomial | rule 28

Édouard Lucas | Ernst Erich Jacobsthal