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 A352426 Maximal number of nonattacking white-square queens on an n X n chessboard. 3
 0, 1, 1, 2, 4, 4, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 49, 50, 51, 51, 52, 53 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Equivalently the maximal number of nonattacking black-square queens on an inverted n X n chessboard, that is a board with the a1 square white, the a2 and b1 squares black, etc. LINKS Andy Huchala, Table of n, a(n) for n = 1..92 Andy Huchala, Python program. Math StackExchange, Black queens on n X n board, 2022. FORMULA a(2n) = A352241(2n). PROG (Python) def fill(rows, queens, leftattack, notdownattack, rightattack, color): global c available = ~leftattack & notdownattack & ~rightattack & color if rows==1: if available==0: c[queens] = c.get(queens, 0) + 1 else: c[queens+1] = c.get(queens+1, 0) + bin(available).count('1') return while available: attack = available & -available fill(rows-1, queens+1, (leftattack|attack)<<1, notdownattack&~attack, (rightattack|attack)>>1, ~color) available &= available - 1 fill(rows-1, queens, leftattack<<1, notdownattack, rightattack>>1, ~color) print(' n a(n) count') for n in range(1, 32): c=dict() fill(n, 0, 0, (1<

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