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A222955
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Number of nX1 0..1 arrays with every row and column least squares fitting to a zero slope straight line, with a single point array taken as having zero slope
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12
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2, 2, 4, 4, 8, 8, 20, 18, 52, 48, 152, 138, 472, 428, 1520, 1392, 5044, 4652, 17112, 15884, 59008, 55124, 206260, 193724, 729096, 688008, 2601640, 2465134, 9358944, 8899700, 33904324, 32342236, 123580884, 118215780, 452902072, 434314138, 1667837680
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OFFSET
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1,1
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COMMENTS
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Conjecture: A binary word is counted iff it has the same sum of positions of 1's as its reverse, or, equivalently, the same sum of partial sums as its reverse. - Gus Wiseman, Jan 07 2023
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LINKS
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EXAMPLE
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All solutions for n=4
..0....1....1....0
..0....1....0....1
..0....1....0....1
..0....1....1....0
The a(1) = 2 through a(7) = 20 binary words with least squares fit a line of zero slope are:
(0) (00) (000) (0000) (00000) (000000) (0000000)
(1) (11) (010) (0110) (00100) (001100) (0001000)
(101) (1001) (01010) (010010) (0010100)
(111) (1111) (01110) (011110) (0011100)
(10001) (100001) (0100010)
(10101) (101101) (0101010)
(11011) (110011) (0110001)
(11111) (111111) (0110110)
(0111001)
(0111110)
(1000001)
(1000110)
(1001001)
(1001110)
(1010101)
(1011101)
(1100011)
(1101011)
(1110111)
(1111111)
(End)
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CROSSREFS
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These words appear to be ranked by A359402.
A359042 adds up partial sums of standard compositions, reversed A029931.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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