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A049828
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Triangular array T given by rows: T(n,k)=sum of remainders when Euclidean algorithm acts on n,k; for k=1,2,...,n; n >= 1.
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8
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0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 3, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 4, 3, 1, 0, 0, 0, 3, 0, 6, 2, 1, 0, 0, 1, 0, 1, 5, 3, 3, 1, 0, 0, 0, 1, 2, 0, 6, 4, 2, 1, 0, 0, 1, 3, 4, 1, 6, 8, 6, 3, 1, 0, 0, 0, 0, 0, 3, 0, 8, 4, 3, 2, 1, 0, 0, 1, 1, 1, 6, 1, 7, 11, 5, 4, 3, 1, 0
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OFFSET
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1,13
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COMMENTS
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For a fixed n, {(k,T(n,k)), k=1..n} is conjectured to be fractal in nature (see link). - Tiberiu Szocs-Mihai, Aug 17 2015
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LINKS
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EXAMPLE
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Rows:
0;
0, 0;
0, 1, 0;
0, 0, 1, 0;
0, 1, 3, 1, 0;
0, 0, 0, 2, 1, 0;
0, 1, 1, 4, 3, 1, 0;
...
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MAPLE
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T:= proc(n, k) option remember;
if n*k = 0 then 0 else (n mod k) + procname(k, n mod k) fi
end proc:
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MATHEMATICA
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T[n_, k_] := T[n, k] = If[n*k == 0, 0, Mod[n, k] + T[k, Mod[n, k]]];
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PROG
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(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, a = n; b = k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s +=r; a = b; b = r); print1(s, ", "); ); print(); ); } \\ Michel Marcus, Aug 17 2015
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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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