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A117906
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Inverse of number triangle A117904.
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3
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1, -1, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Row sums are (1, 0, 1, 0, 0, 0, ...) with g.f. 1 + x^2.
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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 -x^5*y^2)/(1-x^3*y^3).
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EXAMPLE
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Triangle begins
1;
-1, 1;
0, 0, 1;
0, -1, 0, 1;
0, 0, 0, -1, 1;
0, 0, -1, 0, 0, 1;
0, 0, 0, 0, -1, 0, 1;
0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, -1, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1;
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MATHEMATICA
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M[n_, k_]:= M[n, k]= If[k>n, 0, If[Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]==0, 1, 0]];
m:= m= With[{q=20}, Table[M[n, k], {n, 0, q}, {k, 0, q}]];
T[n_, k_]:= Inverse[m][[n+1, k+1]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 20 2021 *)
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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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