Erich, thank you! So it looks like my old A085577 is right after all, and A233735 is wrong. The former has 1, 1, 2, 4, 6, 8, 10, 13, 17, 20, 25, 29, 34 whereas the latter has 1, 1, 2, 4, 6, 8, 10, 13, 16, 20, 25, 29, 34, 39, 45, 52, 58, 65, 72, 80, 88, 96, 105, 114, 124, 134, 144, 155, 166, 178, 190, 202, 215, 228, 242, 256, 270, 285, 300, 316, 332, 348, 365, 382, 400, 418, 436, 455, 474, 494, 514, 534, 555, 576, 598, 620, 642, 665, 688, 712, 736, 760, 785, 810, 836, 862, 888, ... in which the second differences are periodic. Can you confirm (or refute) any other entries? Patrick Ostergard's Clique-finder might be able to handle a few more terms, I guess. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sat, Apr 18, 2015 at 12:53 PM, Erich Friedman <erichfriedman68@gmail.com> wrote:
17 is easy.
.o....o.. ...o....o o....o... ..o....o. ....o.... .o....o.. ...o....o o....o... ..o....o.
erich
To Math Fun: I have been going through old copies of the Popular Computing (Calabasas, CA) newsletter. Problem 178 asks for max number of pieces that can be placed on an nXn chess-board so that no two are closer than a knight's-move apart. See https://oeis.org/a233735_1.pdf for the problem. This can be re-stated as an error-correcting coding question: find max number of cells so that you cannot go from one to another by crossing two edges.
Back in 2003 I seem to have thought that the number for a 9x9 board was 17, as in A085577. But now I can only get 16, which would mean that A085577 is wrong and the true answer is A233735, which even has a remarkably simple explicit formula. Comments, anyone?
Incidentally Bill Gosper gets a nice mention on the same page where the problem is stated (see scan mentioned above).
For other nice problems, mostly unsolved, from Pop. Computing and other old magazines, go to https://oeis.org/A256969 and work backwards through the A-numbers. There is lots of fun to be had here...
Neil _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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