OFFSET
1,1
COMMENTS
Seen as a triangle read by rows: T(n,k) = n mod 2, 1<=k<=n. - Reinhard Zumkeller, Mar 18 2011
Row sums give A193356. - Omar E. Pol, Mar 05 2014
REFERENCES
K. H. Rosen, Discrete Mathematics and its Applications, 1999, Fourth Edition, page 79, exercise 10 (g).
LINKS
Reinhard Zumkeller, Rows n=1..125 of triangle, flattened
FORMULA
a(n) = (1-(-1)^A002024(n))/2, where A002024(n)=round(sqrt(2*n)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003
Also a(n) = A000035(A002024(n)) = A002024(n) mod 2 = A002024(n)-2*floor(A002024(n)/2). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003
G.f.: x/(1-x)*sum_{n>=0} (-1)^n*x^(n*(n+1)/2). - Mircea Merca, Mar 05 2014
a(n) = 1 - A057212(n). - Alois P. Heinz, Oct 06 2021
MAPLE
# alternative Maple program:
T:= n-> [irem(n, 2)$n][]:
seq(T(n), n=1..14); # Alois P. Heinz, Oct 06 2021
MATHEMATICA
Flatten[Table[{PadRight[{}, n, 1], PadRight[{}, n+1, 0]}, {n, 1, 21, 2}]] (* Harvey P. Dale, Jun 07 2015 *)
PROG
(Haskell)
a057211 n = a057211_list !! (n-1)
a057211_list = concat $ zipWith ($) (map replicate [1..]) a059841_list
-- Reinhard Zumkeller, Mar 18 2011
(Python)
from math import isqrt
def A057211(n): return int(bool(isqrt(n<<3)+1&2)) # Chai Wah Wu, Jun 19 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ben Tyner (tyner(AT)phys.ufl.edu), Sep 27 2000
EXTENSIONS
Definition amended by Georg Fischer, Oct 06 2021
STATUS
approved