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).

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, 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, 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

Offset

0,1

Comments

The row sums equal A110654 and the alternating row sums equal A130472. - Johannes W. Meijer, Aug 12 2015

This is also the array:

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 ...

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 ...

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 ...

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 ...

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 ...

0 0 0 0 0 0 0 0 0 0 0 0 0 ...

...

read by antidiagonals. - N. J. A. Sloane, Mar 07 2023

Links

Table of n, a(n) for n=0..104.

Formula

a(n) = A002262(n) mod 2 = A060511(n) mod 2.

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

Example

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.
As a triangle, sequence begins:
0;
0, 1;
0, 1, 0;
0, 1, 0, 1;
0, 1, 0, 1, 0;
0, 1, 0, 1, 0, 1;
...

Maple

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

Mathematica

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 *)

Prog

(Python)
from math import isqrt
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

Crossrefs

As a simple triangular or square array virtually the only sequences which appear are A000004, A000012 and A000035.

Cf. A230135.

Sequence in context: A188037 A144598 A144606 * A327205 A219071 A072629

Adjacent sequences: A060507 A060508 A060509 * A060511 A060512 A060513

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Mar 22 2001

Status

approved