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A108020
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a(n) is the number whose binary representation is the concatenation of n strings of the four digits "1100".
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5
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0, 12, 204, 3276, 52428, 838860, 13421772, 214748364, 3435973836, 54975581388, 879609302220, 14073748835532, 225179981368524, 3602879701896396, 57646075230342348, 922337203685477580, 14757395258967641292, 236118324143482260684, 3777893186295716170956
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OFFSET
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0,2
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COMMENTS
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Numbers whose base-16 representation consists entirely of 12's; 12 times base-16 repunits. - Franklin T. Adams-Watters, Mar 29 2006
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LINKS
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FORMULA
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a(n) = 17*a(n-1) - 16*a(n-2) for n > 1.
G.f.: 12*x / ((1-x)*(1-16*x)).
(End)
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EXAMPLE
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a(3) = 3276 because 3276 written in base 2 is the digit string "1100" written three times: 110011001100.
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MATHEMATICA
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Table[ FromDigits[ Flatten[ Table[{1, 1, 0, 0}, {i, n}]], 2], {n, 0, 16}] (* Robert G. Wilson v, Jun 01 2005 *)
Table[FromDigits[PadRight[{}, 4n, {1, 1, 0, 0}], 2], {n, 0, 20}] (* Harvey P. Dale, Aug 12 2012 *)
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PROG
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(PARI) concat(0, Vec(12*x/((1-x)*(1-16*x)) + O(x^100))) \\ Colin Barker, Dec 06 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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