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A033118
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Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.
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6
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1, 8, 65, 520, 4161, 33288, 266305, 2130440, 17043521, 136348168, 1090785345, 8726282760, 69810262081, 558482096648, 4467856773185, 35742854185480, 285942833483841, 2287542667870728, 18300341342965825, 146402730743726600
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OFFSET
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1,2
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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-2) - 8*a(n-3).
a(n) = 2^(3*n+3)/63 - 1/14 - (-1)^n/18. - R. J. Mathar, Jan 08 2011
G.f. x/((1-x^2)*(1-8*x));
a(n) = (1/3)*Sum_{k=0..n} A001045(3k). (End)
a(n) = floor(8^(n+1)/9)/7 = floor((8*8^n-1)/63) = round((8*8^n-8)/63) = round((16*8^n-9)/63) = ceiling((8*8^n-8)/63). a(n) = a(n-2) + 8^(n-1), n > 2. - Mircea Merca, Dec 28 2010
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MAPLE
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seq(1/7*floor(8^(n+1)/9), n=1..22); # Mircea Merca, Dec 27 2010
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MATHEMATICA
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Table[FromDigits[PadRight[{}, n, {1, 0}], 8], {n, 20}] (* or *) LinearRecurrence[ {8, 1, -8}, {1, 8, 65}, 20] (* Harvey P. Dale, Jan 20 2021 *)
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PROG
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CROSSREFS
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Pairwise sums are (8^n - 1)/7 (A023001).
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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