Trideque Insertion Equation: T[n+1] = T[n] + T[n-1] + T[n-2], where T[n] is the value of the Trideque at index n after an insertion.

Trideque Removal Equation: T[n-1] = T[n] - T[n-1] - T[n-2], where T[n] is the value of the Trideque at index n before a removal.

Trideque Size Equation: Size(T) = Size(T.left) + Size(T.middle) + Size(T.right), where T is a Trideque and Size(T) is the number of elements in the Trideque.

Trideque Access Equation: Access(T, i) = Access(T.left, i) if i < Size(T.left); Access(T.middle, i - Size(T.left)) if Size(T.left) <= i < Size(T.left) + Size(T.middle); Access(T.right, i - Size(T.left) - Size(T.middle)) if i >= Size(T.left) + Size(T.middle), where T is a Trideque and i is the index of the element to access.

Trideque Split Equation: Split(T, i) = (T.left, T.middle, T.right) if i = Size(T.left); (T.left, Split(T.middle, i - Size(T.left)), T.right) if i < Size(T.left) + Size(T.middle); (T.left, T.middle, Split(T.right, i - Size(T.left) - Size(T.middle))) if i >= Size(T.left) + Size(T.middle), where T is a Trideque and i is the index at which to split.

Trideque Merge Equation: Merge(T1, T2) = T1 if Size(T2) = 0; T2 if Size(T1) = 0; Trideque( Merge(T1.left, T2.left), Merge(T1.middle, T2.middle), Merge(T1.right, T2.right)) otherwise, where T1 and T2 are Trideques to be merged.

Trideque Concatenation Equation: Concatenate(T1, T2) = Trideque(T1.left, T1.middle, Merge(T1.right, T2)), where T1 and T2 are Trideques to be concatenated.

Trideque Rotation Equation: Rotate(T, k) = Concatenate(Split(T, k), Split(T, 0)), where T is a Trideque to be rotated and k is the number of positions to rotate.

Trideque Reverse Equation: Reverse(T) = Trideque(Reverse(T.right), Reverse(T.middle), Reverse(T.left)), where T is a Trideque to be reversed.

Trideque Binary Search Equation: BinarySearch(T, x, i, j) = -1 if i > j; i if Access(T, i) = x; BinarySearch(T, x, m+1, j) if Access(T, m) < x; BinarySearch(T, x, i, m-1) if Access(T, m) > x, where T is a sorted Trideque, x is the element to search for, i and j are the left and right indices to search between, and m is the middle index of the Trideque.