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A045996
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Triangles in an n X n grid (or geoplane).
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11
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0, 4, 76, 516, 2148, 6768, 17600, 40120, 82608, 157252, 280988, 477012, 775172, 1214768, 1844512, 2725000, 3930384, 5550844, 7692300, 10482124, 14066996, 18619128, 24337056, 31449200, 40212160, 50921316, 63907468, 79542108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| I. L. Caestro, Checkerboard, sci.math 22 Oct 2000 [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2010]
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FORMULA
| a(n) = ((n - 1)^2*n^2*(n + 1)^2)/6 - 2*Sum(Sum((n - k + 1)*(n - l + 1)*gcd(k - 1, l - 1), k, 2, n), l, 2, n).
a(n) = binomial(n^2,3)- A000938(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 21 2010]
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EXAMPLE
| a(2)=4 because 4 isosceles right triangles can be placed on a 2 X 2 grid.
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MATHEMATICA
| f[n_] := ((n - 1)^2*n^2*(n + 1)^2)/6 - 2*Sum[(n - k + 1)*(n - l + 1)*GCD[k - 1, l - 1], {k, 2, n}, {l, 2, n}]; Array[f, 28] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 23 2010]
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CROSSREFS
| Sequence in context: A067921 A101718 A094160 * A190395 A114453 A093184
Adjacent sequences: A045993 A045994 A045995 * A045997 A045998 A045999
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KEYWORD
| nice,nonn,easy
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AUTHOR
| Ignacio Larrosa Canestro (ignacio.larrosa(AT)eresmas.net)
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