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A117904
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Number triangle [k<=n]*0^abs(L(C(n,2)/3) - L(C(k,2)/3)) where L(j/p) is the Legendre symbol of j and p.
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5
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1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 +x*(1+y) +x^2*y^2 +x^3*y)/((1-x^3)*(1-x^3*y^3)).
T(n, k) = [k<=n] * 2^abs(L(C(n,2)/3) - L(C(k,2)/3)) mod 2.
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EXAMPLE
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Triangle begins
1;
1, 1;
0, 0, 1;
1, 1, 0, 1;
1, 1, 0, 1, 1;
0, 0, 1, 0, 0, 1;
1, 1, 0, 1, 1, 0, 1;
1, 1, 0, 1, 1, 0, 1, 1;
0, 0, 1, 0, 0, 1, 0, 0, 1;
1, 1, 0, 1, 1, 0, 1, 1, 0, 1;
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1;
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MATHEMATICA
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T[n_, k_]:= If[Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]==0, 1, 0];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 20 2021 *)
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PROG
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(Sage)
def A117904(n, k): return 1 if abs(jacobi_symbol(binomial(n, 2), 3) - jacobi_symbol(binomial(k, 2), 3))==0 else 0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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