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A057212
n-th run has length n.
7
0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,1
COMMENTS
T(n,k) = 1 - n mod 2, 1 <= k <= n. [Reinhard Zumkeller, Mar 18 2011]
REFERENCES
K. H. Rosen, Discrete Mathematics and its Applications, 1999, fourth edition, page 79, exercise 10 (g).
FORMULA
a(n)=A003056(n) mod 2 so as a square array T(n, k)=n+k mod 2 - Henry Bottomley, Mar 22 2001
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
a(n)=A163334(n) mod 2 = A163336(n) mod 2 = A163357(n) mod 2 = A163359(n) mod 2, i.e. the array gives the parity of elements at the successive antidiagonals (alternating between 0 and 1) of square arrays constructed from ANY Hilbert curve starting from zero located at the top left corner of a square grid (and using only N,E,S,W steps of length one). - Antti Karttunen, Oct 22 2012
a(n) = 1 - A057211(n). - Alois P. Heinz, Oct 06 2021
MAPLE
A002024 := n->round(sqrt(2*n)):A057212 := n->(1+(-1)^A002024(n))/2;
# alternative Maple program:
T:= n-> [irem(1+n, 2)$n][]:
seq(T(n), n=1..14); # Alois P. Heinz, Oct 06 2021
MATHEMATICA
Table[If[OddQ[n], 0, 1], {n, 1, 14}, {n}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)
PROG
(Haskell)
a057212 n = a057212_list !! (n-1)
a057212_list = concat $ zipWith ($) (map replicate [1..]) a000035_list
-- Reinhard Zumkeller, Mar 18 2011
(Python)
from math import isqrt
def A057212(n): return int(not isqrt(n<<3)+1&2) # Chai Wah Wu, Jun 19 2024
CROSSREFS
Cf. A057211.
As a simple triangular or square array virtually the only sequences which appear are A000004, A000012 and A000035. Cf. A060510.
Sequence in context: A327256 A327177 A366255 * A023959 A341334 A076182
KEYWORD
easy,nonn,tabl
AUTHOR
Ben Tyner (tyner(AT)phys.ufl.edu), Sep 27 2000
STATUS
approved