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A203969 Number of n X 2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

%I A203969 #10 Jul 22 2025 17:41:33
%S A203969 2,7,29,106,396,1488,5569,20859,78133,292644,1096125,4105590,15377699,
%T A203969 57598086,215736791,808054127,3026612006,11336343903,42460908170,
%U A203969 159039700345,595692067467,2231197862121,8357076036219,31301894398172
%N A203969 Number of n X 2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.
%C A203969 Column 2 of A203975.
%H A203969 R. H. Hardin, <a href="/A203969/b203969.txt">Table of n, a(n) for n = 1..210</a>
%F A203969 Empirical: a(n) = 2*a(n-1) +3*a(n-2) +12*a(n-3) +4*a(n-4) +5*a(n-5) -9*a(n-6) -a(n-8) +a(n-9).
%F A203969 Empirical g.f.: x*(2 + 3*x + 9*x^2 + 3*x^3 + 5*x^4 - 8*x^5 - x^7 + x^8) / ((1 + x + x^2 - x^3)*(1 - 3*x - x^2 - 7*x^3 + x^4 + x^6)). - _Colin Barker_, Jun 06 2018
%e A203969 Some solutions for n=5:
%e A203969 ..0..1....0..1....0..1....0..1....0..0....0..0....0..0....0..0....0..0....0..0
%e A203969 ..0..1....1..0....0..0....0..1....1..1....0..0....0..1....1..0....0..1....1..1
%e A203969 ..0..0....0..1....0..1....1..0....0..1....0..1....1..2....2..1....0..1....0..0
%e A203969 ..0..1....0..2....1..0....2..0....0..1....0..1....0..0....0..0....0..0....0..0
%e A203969 ..0..0....0..1....2..0....0..0....1..0....0..1....0..0....0..1....1..1....1..1
%Y A203969 Cf. A203975.
%K A203969 nonn
%O A203969 1,1
%A A203969 _R. H. Hardin_, Jan 08 2012