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A206454
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Number of 0..7 arrays of length n avoiding the consecutive pattern 0..7.
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1
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8, 64, 512, 4096, 32768, 262144, 2097152, 16777215, 134217712, 1073741632, 8589932544, 68719456256, 549755617280, 4398044676096, 35184355311616, 281474825715713, 2251798471507992, 18014386698322304, 144115084996645888, 1152920611253710848, 9223364340274069504
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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) = 8*a(n-1) - a(n-8).
a(n) = Sum_{i=0..floor(n/8)} (-1)^i*8^(n-8*i)*binomial(n-7*i,i).
G.f.: x*(8 - x^7) / (1 - 8*x + x^8). - Colin Barker, Jun 16 2018
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MATHEMATICA
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Table[Sum[(-1)^i*8^(n-8*i)*Binomial[n-7*i, i], {i, 0, Floor[n/8]}], {n, 20}] (* Stefano Spezia, Feb 12 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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STATUS
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approved
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