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A261315
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Number of n-digit positive numbers whose digits occur with equal frequency.
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2
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9, 90, 657, 4788, 27225, 146619, 544329, 2112084, 3447369, 28995255, 9, 1488185631, 9, 73556822205, 38222232057, 3321970172244, 9, 138479121435807, 9, 2209806802214163, 19711054740199689, 28570005, 9, 15574715941421647071, 141378216540777225, 421224309, 9724427617362202602009
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OFFSET
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1,1
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COMMENTS
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a(n) is divisible by 9.
a(n) = 9 if n > 10 is prime.
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LINKS
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FORMULA
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a(n) = (9/10) * Sum_{j | n, j <= 10} n! * ((n/j)!)^(-j) * binomial(10,j).
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EXAMPLE
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For n = 1 there are the numbers 1 to 9.
For n = 2 there are 9 two-digit numbers of the form dd and 81 with two distinct digits, for a total of 90.
For n = 3 there are 9 numbers of the form ddd and 648 with three distinct digits, for a total of 657.
For n = 4 there are 9 numbers of the form dddd, 243 of with two distinct digits each occurring twice, and 4536 with four distinct digits, for a total of 4788.
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MAPLE
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seq(9/10*add(n!/(n/j)!^j * binomial(10, j), j = select(`<=`, numtheory:-divisors(n), 10)), n=1..30);
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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