A036628 Number of 4-ary rooted trees with n nodes and height exactly 4.

0, 0, 0, 0, 1, 3, 8, 18, 35, 65, 114, 194, 316, 510, 793, 1223, 1839, 2737, 3984, 5746, 8123, 11363, 15615, 21212, 28336, 37412, 48597, 62368, 78810, 98359, 120910, 146797, 175601, 207443, 241515, 277666, 314674, 352152, 388503