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A104728
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Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n.
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2
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1, 9, 4, 30, 18, 7, 70, 48, 27, 10, 135, 100, 66, 36, 13, 231, 180, 130, 84, 45, 16, 364, 294, 225, 160, 102, 54, 19, 540, 448, 357, 270, 190, 120, 63, 22, 765, 648, 532, 420, 315, 220, 138, 72, 25, 1045, 900, 756, 616, 483, 360, 250, 156, 81, 28, 1386, 1210, 1035, 864, 700, 546, 405, 280, 174, 90, 31
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OFFSET
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1,2
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COMMENTS
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The triangle is defined as the matrix product A * B, A = [1; 1, 4; 1, 4, 7;...]; B = [1; 2, 1; 3, 2, 1;...]; both infinite lower triangular matrices with the rest of the terms zeros.
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LINKS
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EXAMPLE
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The first few rows of the triangle are:
1;
9, 4;
30, 18, 7;
70, 48, 27, 10;
135, 100, 66, 36, 13;
231, 180, 130, 84, 45, 16;
364, 294, 225, 160, 102, 54, 19;
540, 448, 357, 270, 190, 120, 63, 22;
765, 648, 532, 420, 315, 220, 138, 72, 25;
1045, 900, 756, 616, 483, 360, 250, 156, 81, 28;
1386, 1210, 1035, 864, 700, 546, 405, 280, 174, 90, 31;
1794, 1584, 1375, 1170, 972, 784, 609, 450, 310, 192, 99, 34, etc.
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MAPLE
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(k-1-n)*(k-2-n)*(k-2+2*n)/2 ;
end proc:
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MATHEMATICA
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Table[(k-1-n)(k-2-n)(k-2+2n)/2, {n, 20}, {k, n}]//Flatten (* Harvey P. Dale, Dec 25 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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