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A098011 10^a(n) + 1 = A088773(n). 12
1, 1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Starting from the 4th term, every succeeding term is twice the preceding term. I.e., a(n+1) = 2a(n).

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

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

a(n) for n > 1 are the values used in the variant of the game 2048 called "threes". - Michael De Vlieger, Jul 18 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

David Eppstein, Making Change in 2048, arXiv:1804.07396 [cs.DM], 2018.

Index entries for linear recurrences with constant coefficients, signature (2).

FORMULA

G.f.: x*(1-x-x^3)/(1-2*x). - Paul Barry, Feb 17 2005

a(n) = 3*2^(n-4) for n>3; a(1)=a(2)=1, a(3)=2. - Emeric Deutsch, May 19 2006

a(n) = 2^(n-4)+2^(n-3) for n>3. - Jaroslav Krizek, Aug 17 2009

a(0) = 1, a(2) = 1, a(3) = 2, for n>3: a(n) = sum_(i=2..n-1) a(i). - Jaroslav Krizek, Nov 16 2009

a(n) = A042950(n-3). - Philippe Deléham, Oct 17 2011

a(n) = ceiling(2^{n-2}) - floor(2^{n-4}). - Martin Grymel, Oct 17 2012

MAPLE

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

MATHEMATICA

Table[ Ceiling[3*2^(n - 4)], {n, 34}] (* or *)

Rest@CoefficientList[Series[x(1 - x - x^3)/(1 - 2x), {x, 0, 33}], x] (* Robert G. Wilson v, Jul 08 2006 *)

Table[Ceiling[2^{n-2}]-Floor[2^{n-4}], {n, 1, 10}] (* Martin Grymel, Oct 17 2012 *)

PROG

(PARI) x='x+O('x^99); Vec(x*(1-x-x^3)/(1-2*x)) \\ Altug Alkan, Jul 18 2018

CROSSREFS

Cf. A119440.

Sequence in context: A251745 A251752 A251766 * A110164 A042950 A035055

Adjacent sequences:  A098008 A098009 A098010 * A098012 A098013 A098014

KEYWORD

nonn,easy

AUTHOR

Ray G. Opao, Sep 09 2004

EXTENSIONS

More terms from Emeric Deutsch, May 19 2006

STATUS

approved

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Last modified October 17 21:37 EDT 2019. Contains 328134 sequences. (Running on oeis4.)