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A188707
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Number of 3 X n binary arrays without the pattern 0 0 diagonally or vertically.
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1
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5, 21, 90, 387, 1665, 7164, 30825, 132633, 570690, 2455551, 10565685, 45461772, 195611805, 841673709, 3621533130, 15582644523, 67048623225, 288495182556, 1241330043105, 5341164667857, 22981833209970, 98885672046279
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 3*a(n-2).
G.f.: x*(5 - 4*x)/(1 - 5*x + 3*x^2). - Colin Barker, Mar 11 2012
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EXAMPLE
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Some solutions for 3 X 3:
1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1
1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1
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MATHEMATICA
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PROG
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a(n)=my(v=[1, 1; 1, 4]^(n-1)*[1, 2]~); v[1]*1+v[2]*2; \\ Joerg Arndt, Mar 19 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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