A153983 Number of planar n X n X n binary triangular grids with mirror symmetry about one altitude with every one adjacent to exactly 1 other one.

1, 1, 2, 2, 5, 11, 37, 100, 493, 1878, 13284, 74395, 745275, 5833759, 83605003, 936808185, 19121040653, 305862769758, 8892563071671, 202363258898765, 8388963351859194, 272273853161584435, 16084335957849229172