OFFSET
0,2
COMMENTS
Partial sums of A007910. - Mircea Merca, Dec 27 2010
This is the decimal representation of the middle column of "Rule 54" elementary cellular automaton. - Karl V. Keller, Jr., Sep 26 2021
This same sequence (except that the offset is changed to 4) is 2^n with the final digit chopped off. - J. Lowell, May 11 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-2).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 2*a(n-4), with initial values a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 12.
a(n) = (1/10)*(2^(n+4) + (-1)^floor(n/2) - 2*(-1)^floor((n+1)/2) - 5).
Row sums of A130306. - Gary W. Adamson, May 20 2007
a(n) = floor(2^(n+3)/5). - Gary Detlefs, Sep 06 2010
a(n) = round((2^(n+4)-5)/10) = floor((2^(n+3)-1)/5) = ceiling((2^(n+3)-4)/5) = round((2^(n+3)-2)/5); a(n) = a(n-4) + 3*2^(n-1), n > 3. - Mircea Merca, Dec 27 2010
a(n) = 2^(n+1) - 1 - a(n-2); a(n) = a(n-1)/2 for n == 2, 3 (mod 4); a(n) = (a(n-1)-1)/2 for n == 0, 1 (mod 4). - Arie Bos, Apr 06 2013
a(n) = floor(A000975(n+2)*3/5). - Armands Strazds, Oct 18 2014
a(n) = Sum_{k=1..n+3} floor(1 + sin(k*Pi/2 + 3*Pi/4))*2^(n-k+3). - Andres Cicuttin, Mar 28 2016
a(n) = (-15 + 3*2^(3+n) + 2^(1 + n - 4*floor((1+n)/4)) + 2^(2 + n - 4*floor((2+n)/4)))/15. - Andres Cicuttin, Mar 28 2016
a(n) = (16*2^n+(-1)^((2*n-1+(-1)^n)/4)-2*(-1)^((2*n+1-(-1)^n)/4)-5)/10. - Wesley Ivan Hurt, Apr 01 2016
EXAMPLE
The sequence in hexadecimal shows the pattern
1, 3, 6, c,
19, 33, 66, cc,
199, 333, 666, ccc,
1999, 3333, 6666, cccc,
19999, 33333, 66666, ccccc,
199999, 333333, 666666, cccccc,
1999999, 3333333, 6666666, ccccccc,
19999999, 33333333, 66666666, cccccccc,
... - Armands Strazds, Oct 09 2014
MAPLE
a := proc(n) option remember; if n=0 then RETURN(1); fi; if n=1 then RETURN(3); fi; if n=2 then RETURN(6); fi; if n=3 then RETURN(12); fi; 3*a(n-1)-3*a(n-2)+3*a(n-3)-2*a(n-4); end;
seq(iquo(2^n, 5), n=3..35); # Zerinvary Lajos, Apr 20 2008
MATHEMATICA
CoefficientList[Series[1/((1 - x) (1 - 2 x) (1 + x^2)), {x, 0, 32}], x] (* Michael De Vlieger, Mar 29 2016 *)
LinearRecurrence[{3, -3, 3, -2}, {1, 3, 6, 12}, 40] (* Harvey P. Dale, Feb 06 2019 *)
PROG
(Magma) [Round((2^(n+4)-5)/10): n in [0..40]]; // Vincenzo Librandi, Jun 25 2011
(PARI) a(n)=(16<<n)\10 \\ Charles R Greathouse IV, Sep 23 2012
(PARI) Vec(1/(1-3*x+3*x^2-3*x^3+2*x^4)+O(x^99)) \\ Derek Orr, Oct 26 2014
(Haskell)
import Data.Bits (xor)
a077854 n = a077854_list !! n
a077854_list = scanl1 xor $ tail a000975_list :: [Integer]
-- Reinhard Zumkeller, Jan 04 2013
(Python) print([2**(n+3)//5 for n in range(50)]) # Karl V. Keller, Jr., Sep 26 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved