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A178035
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a(n) is the number of the two-sided n-step prudent walks ending on the top side of their box, avoiding both patterns Left^k and Down^k for k>=3.
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1
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1, 3, 7, 18, 44, 110, 273, 679, 1687, 4191, 10406, 25830, 64097, 159015, 394391, 977939, 2424370, 5977180, 14756906
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