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A263053
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Number of (n+1) X 2 0..1 arrays with each row and column not divisible by 3, read as a binary number with top and left being the most significant bits.
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3
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2, 2, 10, 10, 42, 42, 170, 170, 682, 682, 2730, 2730, 10922, 10922, 43690, 43690, 174762, 174762, 699050, 699050, 2796202, 2796202, 11184810, 11184810, 44739242, 44739242, 178956970, 178956970, 715827882, 715827882, 2863311530, 2863311530
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OFFSET
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1,1
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COMMENTS
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Each row must be either 01 or 10. The two columns are therefore binary complements with sum 2^k-1, where k = n + 1 is the number of rows. If k is even then 2^k-1 is divisible by 3 and the number of solutions is 2*(2^k-1)/3. If k is odd then 2^k-1 == 1 (mod 3) and the number of solutions is (2^k-2)/3. - Andrew Howroyd, Feb 03 2022
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LINKS
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FORMULA
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a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3).
G.f.: 2*x / ((1 - x)*(1 - 2*x)*(1 + 2*x)).
a(n) = 2^n - 2/3 - (-2)^n/3.
(End)
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EXAMPLE
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All solutions for n=4:
0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1
0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0
1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1
0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1
1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1
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PROG
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(Python) [int(2**n - 2/3 -((-2)**n)/3) for n in range(1, 40)] # Pascal Bisson, Feb 03 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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