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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). 4
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 (list; table; graph; refs; listen; history; text; internal format)
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
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 *)
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
KEYWORD
easy,nonn,tabl
AUTHOR
Henry Bottomley, Mar 22 2001
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)