A049675 a(n)=(2*F(3n)-F(n))/3, where F=A000045 (the Fibonacci sequence).

0, 1, 5, 22, 95, 405, 1720, 7293, 30905, 130934, 554675, 2349689, 9953520, 42163913, 178609405, 756601910, 3205017655, 13576673517, 57511713320, 243623529381, 1032005835025, 4371646876246, 18518593350955