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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.

%I A222955 #12 Jul 23 2025 03:18:49
%S A222955 2,2,4,4,8,8,20,18,52,48,152,138,472,428,1520,1392,5044,4652,17112,
%T A222955 15884,59008,55124,206260,193724,729096,688008,2601640,2465134,
%U A222955 9358944,8899700,33904324,32342236,123580884,118215780,452902072,434314138,1667837680
%N 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.
%C A222955 Column 1 of A222959
%C A222955 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 A222955 R. H. Hardin, <a href="/A222955/b222955.txt">Table of n, a(n) for n = 1..210</a>
%e A222955 All solutions for n=4
%e A222955 ..0....1....1....0
%e A222955 ..0....1....0....1
%e A222955 ..0....1....0....1
%e A222955 ..0....1....1....0
%e A222955 From _Gus Wiseman_, Jan 07 2023: (Start)
%e A222955 The a(1) = 2 through a(7) = 20 binary words with least squares fit a line of zero slope are:
%e A222955   (0)  (00)  (000)  (0000)  (00000)  (000000)  (0000000)
%e A222955   (1)  (11)  (010)  (0110)  (00100)  (001100)  (0001000)
%e A222955              (101)  (1001)  (01010)  (010010)  (0010100)
%e A222955              (111)  (1111)  (01110)  (011110)  (0011100)
%e A222955                             (10001)  (100001)  (0100010)
%e A222955                             (10101)  (101101)  (0101010)
%e A222955                             (11011)  (110011)  (0110001)
%e A222955                             (11111)  (111111)  (0110110)
%e A222955                                                (0111001)
%e A222955                                                (0111110)
%e A222955                                                (1000001)
%e A222955                                                (1000110)
%e A222955                                                (1001001)
%e A222955                                                (1001110)
%e A222955                                                (1010101)
%e A222955                                                (1011101)
%e A222955                                                (1100011)
%e A222955                                                (1101011)
%e A222955                                                (1110111)
%e A222955                                                (1111111)
%e A222955 (End)
%Y A222955 These words appear to be ranked by A359402.
%Y A222955 A011782 counts compositions.
%Y A222955 A359042 adds up partial sums of standard compositions, reversed A029931.
%Y A222955 Cf. A053632, A070925, A231204, A318283, A359043.
%K A222955 nonn
%O A222955 1,1
%A A222955 _R. H. Hardin_, Mar 10 2013