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A339184
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Number of partitions of n into two parts such that the larger part is a nonzero square.
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2
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0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET
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0,18
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor(n/2)} c(n-i), where c is the square characteristic (A010052).
a(n) = Sum_{i=floor((n-1)/2)..n-2} c(i+1), where c is the square characteristic (A010052).
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EXAMPLE
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a(8) = 1; The partitions of 8 into 2 parts are (7,1), (6,2), (5,3) and (4,4). Since 4 is the only nonzero square appearing as a largest part, a(8) = 1.
a(9) = 0; The partitions of 9 into 2 parts are (8,1), (7,2), (6,3) and (5,4). Since there are no nonzero squares among the largest parts, a(9) = 0.
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MATHEMATICA
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Table[Sum[Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]] , {i, Floor[n/2]}], {n, 0, 100}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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