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A245989
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Number of length n 0..2 arrays with no pair in any consecutive three terms totalling exactly 2.
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1
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1, 3, 6, 8, 12, 18, 26, 38, 56, 82, 120, 176, 258, 378, 554, 812, 1190, 1744, 2556, 3746, 5490, 8046, 11792, 17282, 25328, 37120, 54402, 79730, 116850, 171252, 250982, 367832, 539084, 790066, 1157898, 1696982, 2487048, 3644946, 5341928, 7828976, 11473922
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OFFSET
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0,2
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COMMENTS
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Also, number of length n ternary words with no pair of equal consecutive letters and avoiding the subwords 010, 101, 020, 202. - Miquel A. Fiol, Dec 22 2023
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3) for n>=5.
G.f.: (x^4 + x^3 + 3*x^2 + 2*x + 1) / (1 - x - x^3). - Colin Barker, Nov 05 2018
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EXAMPLE
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Some solutions for n=12:
0 1 0 1 1 0 2 2 0 2 0 2 0 0 0 1
0 2 1 2 0 0 1 2 1 1 0 2 0 0 1 2
0 2 0 2 0 1 2 1 0 2 0 2 0 0 0 2
0 2 0 1 0 0 2 2 0 2 1 1 1 1 0 1
0 1 1 2 0 0 2 2 0 2 0 2 0 0 0 2
0 2 0 2 1 1 2 1 1 1 0 2 0 0 0 2
0 2 0 2 0 0 1 2 0 2 0 2 0 0 1 2
0 2 0 2 0 0 2 2 0 2 0 2 0 0 0 2
0 1 1 2 1 1 2 1 0 2 0 1 1 0 0 1
0 2 0 1 0 0 2 2 0 2 0 2 0 0 0 2
0 2 0 2 0 0 2 2 0 1 1 2 0 0 0 2
0 2 0 2 1 0 1 1 0 2 0 1 0 0 1 2
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MATHEMATICA
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gf=(x^4 + x^3 + 3*x^2 + 2*x + 1) / (1 - x - x^3); Table[SeriesCoefficient[gf, {x, 0, n}], {n, 0, 40}] (* James C. McMahon, Dec 30 2023 *)
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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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EXTENSIONS
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STATUS
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approved
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