A024223 [ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 3}.

1, 12, 45, 115, 244, 457, 785, 1262, 1926, 2822, 3997, 5504, 7400, 9746, 12608, 16057, 20168, 25021, 30699, 37290, 44888, 53591, 63500, 74722, 87368, 101553, 117397, 135026, 154567, 176154, 199926, 226024, 254597, 285795, 319774, 356694, 396722, 440026