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A108020 a(n) is the number whose binary representation is the concatenation of n strings of the four digits "1100".

%I A108020 #33 Nov 13 2022 08:36:13
%S A108020 0,12,204,3276,52428,838860,13421772,214748364,3435973836,54975581388,
%T A108020 879609302220,14073748835532,225179981368524,3602879701896396,
%U A108020 57646075230342348,922337203685477580,14757395258967641292,236118324143482260684,3777893186295716170956
%N A108020 a(n) is the number whose binary representation is the concatenation of n strings of the four digits "1100".
%C A108020 Numbers whose base-16 representation consists entirely of 12's; 12 times base-16 repunits. - _Franklin T. Adams-Watters_, Mar 29 2006
%H A108020 Colin Barker, <a href="/A108020/b108020.txt">Table of n, a(n) for n = 0..800</a>
%H A108020 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F A108020 a(n) = 12*(16^n - 1)/15. - _Franklin T. Adams-Watters_, Mar 29 2006
%F A108020 From _Colin Barker_, Dec 06 2015: (Start)
%F A108020 a(n) = 17*a(n-1) - 16*a(n-2) for n > 1.
%F A108020 G.f.: 12*x / ((1-x)*(1-16*x)).
%F A108020 (End)
%F A108020 a(n) = 4*A182512(n). - _Jamie Simpson_, Oct 25 2022
%F A108020 a(n) = 12*A131865(n-1) for n>0. - _Hugo Pfoertner_, Nov 01 2022
%e A108020 a(3) = 3276 because 3276 written in base 2 is the digit string "1100" written three times: 110011001100.
%t A108020 Table[ FromDigits[ Flatten[ Table[{1, 1, 0, 0}, {i, n}]], 2], {n, 0, 16}] (* _Robert G. Wilson v_, Jun 01 2005 *)
%t A108020 Table[FromDigits[PadRight[{},4n,{1,1,0,0}],2],{n,0,20}] (* _Harvey P. Dale_, Aug 12 2012 *)
%o A108020 (PARI) concat(0, Vec(12*x/((1-x)*(1-16*x)) + O(x^100))) \\ _Colin Barker_, Dec 06 2015
%o A108020 (PARI) a(n)=12*(16^n - 1)/15 \\ _Charles R Greathouse IV_, Nov 01 2022
%Y A108020 Cf. A131865, A182512.
%K A108020 easy,nonn
%O A108020 0,2
%A A108020 _Alexandre Wajnberg_, May 31 2005
%E A108020 More terms from _Robert G. Wilson v_, Jun 01 2005