Number of ways to arrange 3 nonattacking triangular rooks on an nXnXn triangular grid.

Terms

a(0) =0a(1) =0a(2) =0a(3) =2a(4) =23a(5) =127a(6) =468a(7) =1352a(8) =3310a(9) =7190a(10) =14260a(11) =26330a(12) =45885a(13) =76237a(14) =121688a(15) =187712a(16) =281148a(17) =410412a(18) =585720a(19) =819330a(20) =1125795a(21) =1522235a(22) =2028620a(23) =2668072a(24) =3467178a(25) =4456322a(26) =5670028a(27) =7147322a(28) =8932105a(29) =11073545