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%I #10 Jan 11 2023 08:47:05
%S 2,2,4,4,8,8,20,18,52,48,152,138,472,428,1520,1392,5044,4652,17112,
%T 15884,59008,55124,206260,193724,729096,688008,2601640,2465134,
%U 9358944,8899700,33904324,32342236,123580884,118215780,452902072,434314138,1667837680
%N 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
%C Column 1 of A222959
%C 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
%H R. H. Hardin, <a href="/A222955/b222955.txt">Table of n, a(n) for n = 1..210</a>
%e All solutions for n=4
%e ..0....1....1....0
%e ..0....1....0....1
%e ..0....1....0....1
%e ..0....1....1....0
%e From _Gus Wiseman_, Jan 07 2023: (Start)
%e The a(1) = 2 through a(7) = 20 binary words with least squares fit a line of zero slope are:
%e (0) (00) (000) (0000) (00000) (000000) (0000000)
%e (1) (11) (010) (0110) (00100) (001100) (0001000)
%e (101) (1001) (01010) (010010) (0010100)
%e (111) (1111) (01110) (011110) (0011100)
%e (10001) (100001) (0100010)
%e (10101) (101101) (0101010)
%e (11011) (110011) (0110001)
%e (11111) (111111) (0110110)
%e (0111001)
%e (0111110)
%e (1000001)
%e (1000110)
%e (1001001)
%e (1001110)
%e (1010101)
%e (1011101)
%e (1100011)
%e (1101011)
%e (1110111)
%e (1111111)
%e (End)
%Y These words appear to be ranked by A359402.
%Y A011782 counts compositions.
%Y A359042 adds up partial sums of standard compositions, reversed A029931.
%Y Cf. A053632, A070925, A231204, A318283, A359043.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 10 2013
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