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A336430
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Number of partitions of n into two positive integer parts that have the same number of decimal digits.
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0
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0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/2)} [floor(log_10(k)) = floor(log_10(n-k))], where [ ] is the Iverson bracket.
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EXAMPLE
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a(11) = 4; There are 5 partitions of 11 into two parts, (10,1), (9,2), (8,3), (7,4) and (6,5). Only 4 of these partitions have the same number of decimal digits, so a(11) = 4.
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MATHEMATICA
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Table[Sum[KroneckerDelta[Floor[Log10[i]], Floor[Log10[n - i]]], {i, Floor[n/2]}], {n, 100}]
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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