A function is to be constructed that, given an input of a positive integer value m, automatically enumerates all possible cases. Starting with an arithmetic sequence of length 4*m + 2, two terms are removed leaving 4m terms, which are then evenly divided into m groups, each consisting of 4 numbers. It is required that the 4 numbers in each group form their own arithmetic sequence. The function should generate all combinations of the two removed terms and the corresponding m groups of four numbers forming arithmetic sequences.
To clarify the problem statement further, let's break down the requirements:
- An arithmetic sequence of length 4*m + 2 is created.
- Two terms from this sequence are removed.
- The remaining 4m terms are divided into m groups, each containing exactly 4 terms.
- Each of these groups must also be an arithmetic sequence.
- The function should output all possible combinations of the two removed terms and the resulting groups of four numbers that form arithmetic sequences.
f[m_Integer] :=
Module[{originalSequence, deletedPairs, remainingSequence,
subSequences}, originalSequence = Range[4*m + 2];
deletedPairs = Subsets[originalSequence, {2}];
remainingSequence = {};
subSequences = {};
Do[remainingSequence = Complement[originalSequence, deletedPair];
If[Length[remainingSequence] == 4*m,
subSequences = Partition[remainingSequence, 4];
If[AllTrue[subSequences, Differences[#] === {1, 1, 1} &],
Print["Deleted pair: ", deletedPair];
Print["Subsequences: ", subSequences];]], {deletedPair,
deletedPairs}];]
After providing the corresponding positive integer value of m, the above code has missing sequence issues upon execution, how should the code be modified?