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A222955
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
12
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
OFFSET
1,1
COMMENTS
Column 1 of A222959
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
LINKS
EXAMPLE
All solutions for n=4
..0....1....1....0
..0....1....0....1
..0....1....0....1
..0....1....1....0
From Gus Wiseman, Jan 07 2023: (Start)
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)
CROSSREFS
These words appear to be ranked by A359402.
A011782 counts compositions.
A359042 adds up partial sums of standard compositions, reversed A029931.
Sequence in context: A158780 A231208 A306663 * A217208 A287136 A351788
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 10 2013
STATUS
approved