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Let an be the number of n-digit strings, consisting only of even digits 0,2,4,6,8 and such that the number of 2s is odd and the
Let an be the number of n-digit strings, consisting only of even digits 0,2,4,6,8 and such that the number of 2s is odd and the number of 4s is odd. Here ao = 0. (a) Find an expression for the exponential generating function of (an) in terms of exponential functions. (b) Use (a) to find a simple exact formula for an (not involving a summation). Let an be the number of n-digit strings, consisting only of even digits 0,2,4,6,8 and such that the number of 2s is odd and the number of 4s is odd. Here ao = 0. (a) Find an expression for the exponential generating function of (an) in terms of exponential functions. (b) Use (a) to find a simple exact formula for an (not involving a summation)
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