This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A077435 Number of right triangles whose vertices are lattice points in {1,2,...,n} X {1,2,...,n}. 9
 0, 4, 44, 200, 596, 1444, 2960, 5520, 9496, 15332, 23596, 34936, 50020, 69732, 94816, 126176, 164960, 212372, 269620, 337960, 418716, 513444, 623736, 751152, 897776, 1065220, 1255460, 1470680, 1713052, 1984564, 2288304, 2626160, 3000960, 3415124, 3871108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It would be nice to have a formula. - N. J. A. Sloane, Jun 29 2016 Place all bounding boxes of A279433 that will fit into the n X n grid in all possible positions, and the proper rectangles in two orientations: a(n) = sum(i=1..n, sum(j=1..i, k * (n-i+1) * (n-j+1) * A279433(i,j) where k=1 when i=j and k=2 otherwise. - Lars Blomberg, Mar 01 2017 LINKS Lars Blomberg, Table of n, a(n) for n = 1..10000 (the first 184 terms from R. H. Hardin) EXAMPLE For n=2 if the four points are labeled ab cd then the right triangles are abc, abd, acd, bcd, so a(2)=4. For n=3, label the points abc def ghi The right triangles are: abd (4*4 ways), acg (4 ways), acd and adf (8 ways each), ace and dbf (4 ways each), for a total of a(3) = 44. - N. J. A. Sloane, Jun 30 2016 CROSSREFS Cf. A187452, A279433. Sequence in context: A053314 A051223 A265081 * A271294 A269907 A270130 Adjacent sequences:  A077432 A077433 A077434 * A077436 A077437 A077438 KEYWORD nonn AUTHOR John W. Layman, Nov 30 2002 EXTENSIONS a(1) corrected by Lars Blomberg, Mar 01 2017 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.