SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\HigherRank"];
<< theta.m

Expand@θ[Knot[3,1]]

TestSymmetries[Knot[3,1]]

NumberOfKnots[10, Alternating] = 123
NumberOfKnots[11, Alternating] = 367
NumberOfKnots[12, Alternating] = 1288
NumberOfKnots[13, Alternating] = 4878
NumberOfKnots[14, Alternating] = 19536
NumberOfKnots[15, Alternating] = 85263
NumberOfKnots[16, Alternating] = 379799

NumberOfKnots[10, NonAlternating] = 42
NumberOfKnots[11, NonAlternating] = 185
NumberOfKnots[12, NonAlternating] = 888
NumberOfKnots[13, NonAlternating] = 5110
NumberOfKnots[14, NonAlternating] = 27436
NumberOfKnots[15, NonAlternating] = 168030
NumberOfKnots[16, NonAlternating] = 1008906

AbsoluteTiming[Monitor[
tab14=Table[K->Expand@θ@K,{K,AllKnots[{3,14}] }],
K]]

Put[tab14/.{(Subscript[T, 1])->T1,(Subscript[T, 2])->T2}, "Data14.m"]

dup14=Map[First,Select[Gather[tab14,Last[#1]===Last[#2]&], Length[#]>1&],{2}]

Sort[Length/@dup14]

Total[(Length/@dup14)-1]

dup14Q=Map[First,Select[Gather[tab14/.{(Subscript[T, 1])->I,(Subscript[T, 2])->I},Last[#1]===Last[#2]&], Length[#]>1&],{2}]

Total[(Length/@dup14Q)-1]

dup14Q=Map[First,Select[Gather[tab14/.{(Subscript[T, 1])->22/7,(Subscript[T, 2])->34/21},Last[#1]===Last[#2]&], Length[#]>1&],{2}]

Total[(Length/@dup14Q)-1]

AbsoluteTiming[Monitor[
tab15Q=Table[K->(Subscript[θ, 22/7,34/21])@K,{K,AllKnots[{3,15}] }],
K]]

dup15Q=Map[First,Select[Gather[tab15Q,Last[#1]===Last[#2]&], Length[#]>1&],{2}]

Total[(Length/@dup15Q)-1]