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 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)
 OFFSET 1,3 COMMENTS 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): OOOOOOOOOOOOOOOOOOOOO -OOOOOOOOOOOOOOOOOOO- --OOOOOOOOOOOOOOOOO-- ---OOOOOOOOOOOOOOO--- ----OOOOOOOOOOOOO---- -----OOOOOOOOOOO----- ------OOOOOOOOO------ -------OOOOOOO------- --------OOOOO-------- ---------OOO--------- ----------O---------- 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 LINKS FORMULA 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 EXAMPLE For n=6 the maximal number is 5: OOXOOOOOOOO -OOOOOOXOO- --OXOOOOO-- ---OOOXO--- ----OOO---- -----X----- Examples from Rob Pratt, Jul 13 2016: (i) For n=15 the maximal number is 13: OOOOOOXOOOOOOOOOOOOOOOOOOOOOO -OOOOOOOOOOOOOOOOOOXOOOOOOOO- --OOOOOXOOOOOOOOOOOOOOOOOOO-- ---OOOOOOOOOOOOOOOXOOOOOOO--- ----OOOOOOOOOOOXOOOOOOOOO---- -----OOOOOOOXOOOOOOOOOOO----- ------OOOXOOOOOOOOOOOOO------ -------OOOOOOOOOXOOOOO------- --------OOXOOOOOOOOOO-------- ---------OOOOOOOOXOO--------- ----------OOOOXOOOO---------- -----------XOOOOOO----------- ------------OXOOO------------ -------------OOO------------- --------------O-------------- (ii) For n=31 the maximal number is 28: OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOO -OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOO- --OOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO-- ---OOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO--- ----OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOO---- -----OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOO----- ------OOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO------ -------OOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO------- --------OOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOO-------- ---------OOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOO--------- ----------OOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOO---------- -----------OOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOO----------- ------------OOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOO------------ -------------OOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOO------------- --------------OOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOO-------------- ---------------OOOOOXOOOOOOOOOOOOOOOOOOOOOOOOO--------------- ----------------OOOOOOOXOOOOOOOOOOOOOOOOOOOOO---------------- -----------------OOOOOOOOOOOOOOOOOOOXOOOOOOO----------------- ------------------OOOOXOOOOOOOOOOOOOOOOOOOO------------------ -------------------OOOOOOOOOOOOOOOOXOOOOOO------------------- --------------------OXOOOOOOOOOOOOOOOOOOO-------------------- ---------------------OOOOOOOOOOOOOXOOOOO--------------------- ----------------------OOOOOOOOXOOOOOOOO---------------------- -----------------------OOOXOOOOOOOOOOO----------------------- ------------------------OOOOOOOOOXOOO------------------------ -------------------------XOOOOOOOOOO------------------------- --------------------------OOOOOOXOO-------------------------- ---------------------------OOXOOOO--------------------------- ----------------------------OOOOO---------------------------- -----------------------------OOO----------------------------- ------------------------------O------------------------------ CROSSREFS Cf. A274616, A287864, A287866. Sequence in context: A291041 A291766 A291579 * A080331 A297247 A167463 Adjacent sequences:  A274930 A274931 A274932 * A274934 A274935 A274936 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Jul 13 2016 EXTENSIONS Terms a(n) with n >= 15 corrected and extended by Rob Pratt, Jul 13 2016 STATUS approved

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