|
%I #29 Jun 19 2024 10:37:42
%S 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,
%T 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,
%U 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
%N n-th run has length n.
%C T(n,k) = 1 - n mod 2, 1 <= k <= n. [_Reinhard Zumkeller_, Mar 18 2011]
%D K. H. Rosen, Discrete Mathematics and its Applications, 1999, fourth edition, page 79, exercise 10 (g).
%F a(n)=A003056(n) mod 2 so as a square array T(n, k)=n+k mod 2 - _Henry Bottomley_, Mar 22 2001
%F 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
%F 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
%F a(n) = 1 - A057211(n). - _Alois P. Heinz_, Oct 06 2021
%p A002024 := n->round(sqrt(2*n)):A057212 := n->(1+(-1)^A002024(n))/2;
%p # alternative Maple program:
%p T:= n-> [irem(1+n, 2)$n][]:
%p seq(T(n), n=1..14); # _Alois P. Heinz_, Oct 06 2021
%t Table[If[OddQ[n], 0, 1], {n, 1, 14}, {n}] // Flatten (* _Jean-François Alcover_, Mar 07 2021 *)
%o (Haskell)
%o a057212 n = a057212_list !! (n-1)
%o a057212_list = concat $ zipWith ($) (map replicate [1..]) a000035_list
%o -- _Reinhard Zumkeller_, Mar 18 2011
%o (Python)
%o from math import isqrt
%o def A057212(n): return int(not isqrt(n<<3)+1&2) # _Chai Wah Wu_, Jun 19 2024
%Y Cf. A057211.
%Y As a simple triangular or square array virtually the only sequences which appear are A000004, A000012 and A000035. Cf. A060510.
%K easy,nonn,tabl
%O 1,1
%A Ben Tyner (tyner(AT)phys.ufl.edu), Sep 27 2000
|
