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A218836 Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.

%I A218836 #33 Jan 29 2025 07:53:50
%S A218836 1,2,7,21,65,200,616,1897,5842,17991,55405,170625,525456,1618192,
%T A218836 4983377,15346786,47261895,145547525,448227521,1380359512,4250949112,
%U A218836 13091204281,40315615410,124155792775,382349636061,1177482265857,3626169232672,11167134898976
%N A218836 Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.
%H A218836 R. H. Hardin, <a href="/A218836/b218836.txt">Table of n, a(n) for n = 0..210</a>
%H A218836 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,1).
%F A218836 a(n) = 2*a(n-1) +3*a(n-2) +a(n-3).
%F A218836 G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1- x*(4*k+2 +3*x+x^2)/(x*(4*k+4 +3*x+x^2) + 1/Q(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Oct 04 2013
%F A218836 G.f.: 1/(1-2*x-3*x^2-x^3). - _Alois P. Heinz_, Apr 21 2020
%e A218836 Some solutions for n=3
%e A218836 ..1..1....1..1....0..0....1..0....0..0....1..0....0..0....1..1....0..0....1..0
%e A218836 ..1..1....1..1....0..1....0..1....0..0....0..0....0..0....0..0....0..1....0..0
%e A218836 ..1..1....0..0....0..0....1..1....0..1....1..1....1..1....1..1....1..1....0..1
%p A218836 a:= n-> (<<0|1|0>, <0|0|1>, <1|3|2>>^n. <<1, 2, 7>>)[1$2]:
%p A218836 seq(a(n), n=0..30);  # _Alois P. Heinz_, Apr 21 2020
%t A218836 LinearRecurrence[{2, 3, 1}, {1, 2, 7}, 30] (* _Paolo Xausa_, Jan 29 2025 *)
%Y A218836 Column 2 of A218842.
%K A218836 nonn,easy
%O A218836 0,2
%A A218836 _R. H. Hardin_, Nov 07 2012
%E A218836 a(0)=1 prepended and first g.f. adapted by _Alois P. Heinz_, Apr 21 2020