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A060510
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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).
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4
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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
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OFFSET
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0,1
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COMMENTS
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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 ...
...
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LINKS
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FORMULA
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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
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EXAMPLE
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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;
...
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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As a simple triangular or square array virtually the only sequences which appear are A000004, A000012 and A000035.
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KEYWORD
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AUTHOR
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STATUS
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approved
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