A144057 Number of n X n binary arrays, symmetric about the diagonal and under 90 degree rotation, with every 1 adjacent to at least one other 1, but at most one 1 adjacent horizontally and at most one 1 adjacent vertically.

1, 2, 1, 3, 5, 13, 23, 83, 158, 743, 1983, 10973, 39092, 269179, 1193276, 10361962, 58314051, 622131402, 4633595266, 60891994633, 582192966557, 9528749362116, 116024808662011, 2351972316090989, 37180717253935256, 930816997530667262