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A332353
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Triangle read by rows: T(m,n) = Sum_{-m<i<m, -n<j<n, gcd{i,j}=2} (m-|i|)*(n-|j|)/2, m >= n >= 1.
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2
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0, 0, 0, 1, 2, 8, 2, 4, 14, 24, 3, 6, 22, 38, 60, 4, 8, 30, 52, 82, 112, 5, 10, 40, 70, 112, 154, 212, 6, 12, 50, 88, 142, 196, 270, 344, 7, 14, 62, 110, 178, 246, 340, 434, 548, 8, 16, 74, 132, 214, 296, 410, 524, 662, 800, 9, 18, 88, 158, 258, 358, 498, 638, 808, 978, 1196
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OFFSET
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1,5
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COMMENTS
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This is the triangle in A332352, halved.
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LINKS
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EXAMPLE
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Triangle begins:
0,
0, 0,
1, 2, 8,
2, 4, 14, 24,
3, 6, 22, 38, 60,
4, 8, 30, 52, 82, 112,
5, 10, 40, 70, 112, 154, 212,
6, 12, 50, 88, 142, 196, 270, 344,
7, 14, 62, 110, 178, 246, 340, 434, 548,
8, 16, 74, 132, 214, 296, 410, 524, 662, 800,
...
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MAPLE
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VR := proc(m, n, q) local a, i, j; a:=0;
for i from -m+1 to m-1 do for j from -n+1 to n-1 do
if gcd(i, j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end;
for m from 1 to 12 do lprint(seq(VR(m, n, 2)/2, n=1..m), ); od:
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MATHEMATICA
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A332353[m_, n_]:=Sum[If[GCD[i, j]==2, 2(m-i)(n-j), 0], {i, 2, m-1, 2}, {j, 2, n-1, 2}]+If[n>2, m*n-2m, 0]+If[m>2, m*n-2n, 0]; Table[A332353[m, n], {m, 15}, {n, m}] (* Paolo Xausa, Oct 18 2023 *)
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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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