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Find the Generating Function to Combinatorial Problems
Find the generating function for the number of 0,1 sequences of length n with two adjacent 1s.
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Click for copyable input
Table[Count[Tuples[{1, 0}, n], {___, 1, 1, ___}], {n, 10}]
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In[2]:=

Click for copyable input
Table[Count[Tuples[{1, 0}, n], {___, 1, 1, ___}], {n, 10}];

FindGeneratingFunction[%, x]
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In[3]:=

Click for copyable input
Table[Count[Tuples[{1, 0}, n], {___, 1, 1, ___}], {n, 10}];

FindGeneratingFunction[%, x];

Table[Count[Tuples[{1, 0}, n], {___, 1, 1, ___}], {n, 20}] - 

 CoefficientList[Series[%, {x, 0, 19}], x]
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