This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A045996 Number of triangles in an n X n grid (or geoplane). 17
 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; text; internal format)
 OFFSET 1,2 COMMENTS The triangles must have nonzero area - their vertices must not be collinear. LINKS I. L. Canestro, Checkerboard, sci.math 22 Oct 2000 [broken link] I. L. Canestro, Checkerboard, sci.math 22 Oct 2000 [Cached copy] 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). - R. J. Mathar, May 21 2010 EXAMPLE a(2)=4 because 4 isosceles right triangles can be placed on a 2 X 2 grid. 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] (* Robert G. Wilson v, May 23 2010 *) CROSSREFS Sequence in context: A317903 A101718 A094160 * A190395 A240281 A114453 Adjacent sequences:  A045993 A045994 A045995 * A045997 A045998 A045999 KEYWORD nice,nonn,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 19 10:50 EST 2018. Contains 318246 sequences. (Running on oeis4.)