A049674 a(n)=(F(3n)-2*F(n))/6, where F=A000045 (the Fibonacci sequence).

0, 0, 1, 5, 23, 100, 428, 1820, 7721, 32725, 138655, 587400, 2488344, 10540920, 44652257, 189150325, 801254167, 3394167980, 14377927684, 60905881300, 258001457065, 1092911716325, 4629648333311, 19611505067280