A183726 1/12 the number of (n+1) X 7 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

3070, 41423, 525895, 7319684, 112949014, 2740758406, 134020420595, 9546147995730, 729082624201394, 55559473375122011, 4177316401273489526, 310180873007618124181, 22791464284740341972598, 1660173775969136404275224