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A189416
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Number of parallelograms on an n X n grid.
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4
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0, 1, 22, 158, 674, 2159, 5664, 13004, 26904, 51401, 92094, 156710, 255090, 400359, 608656, 900100, 1299336, 1836461, 2546550, 3472162, 4661898, 6173123, 8071952, 10434600, 13346080, 16905033, 21221558, 26419338, 32636098, 40027283, 48761448
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{a=1..n-1} Sum_{b=1..n-1} (n-a)*(n-b)*(2*a*b - gcd(a,b)). - Andrew Howroyd, Sep 19 2017
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MATHEMATICA
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a[n_] := Sum[(n-a)*(n-b)*(2*a*b - GCD[a, b]), {a, 1, n-1}, {b, 1, n-1}];
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PROG
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(PARI) a(n) = sum(a=1, n-1, sum(b=1, n-1, (n-a)*(n-b)*(2*a*b - gcd(a, b)) )); \\ Andrew Howroyd, Sep 19 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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