This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274933 Maximal number of non-attacking queens on a quarter chessboard containing n^2 squares. 3
1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42 (list; graph; refs; listen; history; text; internal format)



Take the quarter-board formed from a 2n-1 X 2n-1 chessboard by joining the center square to the top two corners. There are n^2 squares. If n = 11, 2n-1 = 21 and the board looks like this, with 11^2 = 121 squares (the top row is the top of the chessboard, the single cell at the bottom is at the center of the board):












The main question is, how does a(n) behave when n is large? (See A287866.)

This is a bisection of A287864. - Rob Pratt, Jun 04 2017


Table of n, a(n) for n=1..45.


Since there can be at most one queen per row, a(n) <= n. In fact, since there cannot be a queen on both rows 1 and 2, a(n) <= n-1 for n>1. - N. J. A. Sloane, Jun 04 2017


For n=6 the maximal number is 5:







Examples from Rob Pratt, Jul 13 2016:

(i) For n=15 the maximal number is 13:
















(ii) For n=31 the maximal number is 28:

































Cf. A274616, A287864, A287866.

Sequence in context: A291041 A291766 A291579 * A080331 A297247 A167463

Adjacent sequences:  A274930 A274931 A274932 * A274934 A274935 A274936




N. J. A. Sloane, Jul 13 2016


Terms a(n) with n >= 15 corrected and extended by Rob Pratt, Jul 13 2016



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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)