cp's OEIS Frontend

A060510 Alternating with hexagonal stutters: if n is hexagonal (2k^2 - k, i.e., A000384) then a(n)=a(n-1), otherwise a(n) = 1 - a(n-1).

%I A060510 #22 Oct 23 2024 16:32:53
%S A060510 0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,
%T A060510 0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,
%U A060510 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1
%N A060510 Alternating with hexagonal stutters: if n is hexagonal (2k^2 - k, i.e., A000384) then a(n)=a(n-1), otherwise a(n) = 1 - a(n-1).
%C A060510 The row sums equal A110654 and the alternating row sums equal A130472. - _Johannes W. Meijer_, Aug 12 2015
%C A060510 This is also the array:
%C A060510   0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C A060510   1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%C A060510   0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C A060510   1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%C A060510   0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C A060510   1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%C A060510   0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C A060510   1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%C A060510   0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C A060510   1 1 1 1 1 1 1 1 1 1 1 1 1 ...
%C A060510   0 0 0 0 0 0 0 0 0 0 0 0 0 ...
%C A060510   ...
%C A060510 read by antidiagonals. - _N. J. A. Sloane_, Mar 07 2023
%F A060510 a(n) = A002262(n) mod 2 = A060511(n) mod 2.
%F A060510 G.f.: x/(1-x^2) - (1+x)^(-1)*Sum(n>=1, x^(n*(2*n-1))). The sum is related to Theta functions. - _Robert Israel_, Aug 12 2015
%e A060510 Hexagonal numbers start 1,6,15, ... so this sequence goes 0 0 (stutter at 1) 1 0 1 0 0 (stutter at 6) 1 0 1 0 1 0 1 0 0 (stutter at 15) 1 0, etc.
%e A060510 As a triangle, sequence begins:
%e A060510 0;
%e A060510 0, 1;
%e A060510 0, 1, 0;
%e A060510 0, 1, 0, 1;
%e A060510 0, 1, 0, 1, 0;
%e A060510 0, 1, 0, 1, 0, 1;
%e A060510 ...
%p A060510 T := proc(n, k): if k mod 2 = 1 then return(1) else return(0) fi: end: seq(seq(T(n, k), k=0..n), n=0..13);  # _Johannes W. Meijer_, Aug 12 2015
%t A060510 nxt[{n_,a_}]:={n+1,If[IntegerQ[(1+Sqrt[1+8(n+1)])/4],a,1-a]}; NestList[ nxt,{0,0},110][[All,2]] (* _Harvey P. Dale_, Jan 13 2022 *)
%o A060510 (Python)
%o A060510 from math import isqrt
%o A060510 def A060510(n): return n+1&1^1^((m:=isqrt(n+1<<3)+1>>1)*(m-1)>>1&1) # _Chai Wah Wu_, Oct 23 2024
%Y A060510 As a simple triangular or square array virtually the only sequences which appear are A000004, A000012 and A000035.
%Y A060510 Cf. A230135.
%K A060510 easy,nonn,tabl
%O A060510 0,1
%A A060510 _Henry Bottomley_, Mar 22 2001