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%I #19 Oct 11 2022 21:41:25
%S 0,3,4,20,48,175,512,1719,5400,17776,57420,188656,617176,2033175,
%T 6697744,22139780,73262232,242931321,806516560,2681475048,8925158440,
%U 29740390672,99196158144,331163178475,1106489052968,3699881730900,12380449027324
%N Number of nX2 0..1 arrays with exactly floor(nX2/2) elements unequal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..1 order
%C From _Gus Wiseman_, Oct 05 2022: (Start)
%C Conjecture: Also the number of integer compositions of 2n + 1 with the same length as reverse-alternating sum. Here, the reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i. For example, the a(4) = 20 compositions are:
%C (135) (234) (333) (432) (531)
%C (11115) (21114) (31113) (41112) (51111)
%C (11214) (21213) (31212) (41211)
%C (11313) (21312) (31311)
%C (11412) (21411)
%C (11511)
%C This is the odd-indexed version of A357182, and the corresponding unordered count (partitions) is A357488.
%C (End)
%H R. H. Hardin, <a href="/A222763/b222763.txt">Table of n, a(n) for n = 1..210</a>
%e All solutions for n=3
%e ..0..1....0..0....0..0....0..0
%e ..0..0....0..0....0..1....1..0
%e ..0..0....1..0....0..0....0..0
%Y Column k = 2 of A222769.
%K nonn
%O 1,2
%A _R. H. Hardin_ Mar 05 2013
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