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A083023
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a(n) = number of partitions of n into a pair of parts n=p+q, p>=q>=0, with p-q equal to a square >= 0.
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1
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1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6
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OFFSET
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1,4
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COMMENTS
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Number of integers k, 0 <= k <= n/2 such that n - 2k is a square.
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LINKS
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FORMULA
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See Maple line.
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EXAMPLE
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a(11) = 2: the partitions are (1,10) and (5,6).
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MAPLE
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f := n->if n mod 2 = 0 then floor(sqrt((n-2)/4))+1 else floor(sqrt((n-2)/4)-1/2)+1; fi; # then add 1 if n is a square!
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PROG
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(PARI)
a(n)={my(ct=0, d=0); while(d^2<=n, if((n-d^2)%2==0, ct+=1); d+=1 ); return(ct); }
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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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Anne M. Donovan (anned3005(AT)aol.com), May 31 2003
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EXTENSIONS
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STATUS
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approved
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