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%I #37 Nov 16 2019 01:40:27
%S 1,1,2,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,24576,49152,
%T 98304,196608,393216,786432,1572864,3145728,6291456,12582912,25165824,
%U 50331648,100663296,201326592,402653184,805306368,1610612736,3221225472
%N 10^a(n) + 1 = A088773(n).
%C Starting from the 4th term, every succeeding term is twice the preceding term. I.e., a(n+1) = 2a(n).
%C Number of binary words of length n-2 that do not start with 01 (n>=2). Example: a(5)=6 because we have 000,001,100,101,110 and 111. Except for the initial term, column 0 of A119440. - _Emeric Deutsch_, May 19 2006
%C a(n) written in base 2: a(1) = 1, a(2) = 1, a(3) = 10, a(n) for n >= 4: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, (n-4) times 0 (see A003953(n-3). - _Jaroslav Krizek_, Aug 17 2009
%C a(n) for n > 1 are the values used in the variant of the game 2048 called "threes". - _Michael De Vlieger_, Jul 18 2018
%H Vincenzo Librandi, <a href="/A098011/b098011.txt">Table of n, a(n) for n = 1..1000</a>
%H David Eppstein, <a href="https://arxiv.org/abs/1804.07396">Making Change in 2048</a>, arXiv:1804.07396 [cs.DM], 2018.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F G.f.: x*(1 - x - x^3)/(1 - 2*x). - _Paul Barry_, Feb 17 2005
%F a(n) = 3*2^(n-4) for n>3; a(1)=a(2)=1, a(3)=2. - _Emeric Deutsch_, May 19 2006
%F a(n) = 2^(n-4) + 2^(n-3) for n > 3. - _Jaroslav Krizek_, Aug 17 2009
%F a(1) = 1, a(2) = 1, a(3) = 2, for n > 3: a(n) = Sum_{i = 2..n-1} a(i). - _Jaroslav Krizek_, Nov 16 2009 [Corrected by _Petros Hadjicostas_, Nov 16 2019]
%F a(n) = A042950(n-3). - _Philippe Deléham_, Oct 17 2011
%F a(n) = ceiling(2^{n-2}) - floor(2^{n-4}). - _Martin Grymel_, Oct 17 2012
%p a:=proc(n) if n=1 or n=2 then 1 elif n=3 then 2 else 3*2^(n-4) fi end: seq(a(n),n=1..37); # _Emeric Deutsch_, May 19 2006
%t Table[ Ceiling[3*2^(n - 4)], {n, 34}] (* or *)
%t Rest@CoefficientList[Series[x(1 - x - x^3)/(1 - 2x), {x, 0, 33}], x] (* _Robert G. Wilson v_, Jul 08 2006 *)
%t Table[Ceiling[2^{n-2}]-Floor[2^{n-4}],{n,1,10}] (* _Martin Grymel_, Oct 17 2012 *)
%o (PARI) x='x+O('x^99); Vec(x*(1-x-x^3)/(1-2*x)) \\ _Altug Alkan_, Jul 18 2018
%Y Cf. A119440.
%K nonn,easy
%O 1,3
%A _Ray G. Opao_, Sep 09 2004
%E More terms from _Emeric Deutsch_, May 19 2006
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