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A176270
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Triangle T(n,m) = 1 + m*(m-n) read by rows, 0 <= m <= n.
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2
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1, 1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -2, -3, -2, 1, 1, -3, -5, -5, -3, 1, 1, -4, -7, -8, -7, -4, 1, 1, -5, -9, -11, -11, -9, -5, 1, 1, -6, -11, -14, -15, -14, -11, -6, 1, 1, -7, -13, -17, -19, -19, -17, -13, -7, 1, 1, -8, -15, -20, -23, -24, -23, -20, -15, -8, 1
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OFFSET
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0,12
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COMMENTS
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For GCD(-1 - m,-1 - n + m) = 1, smallest number that cannot be written as a*(-1 - m) + b*(-1 - n + m) with a and b in the nonnegative integers. - Thomas Anton, May 22 2019
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LINKS
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FORMULA
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T(n,m) = binomial(n-m+1,2) + binomial(m+1,2) - binomial(n+1,2) + 1 = m^2 - n*m + 1.
T(n,m) = T(n,n-m).
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EXAMPLE
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Triangle begins
1;
1, 1;
1, 0, 1;
1, -1, -1, 1;
1, -2, -3, -2, 1;
1, -3, -5, -5, -3, 1;
1, -4, -7, -8, -7, -4, 1;
1, -5, -9, -11, -11, -9, -5, 1;
1, -6, -11, -14, -15, -14, -11, -6, 1;
1, -7, -13, -17, -19, -19, -17, -13, -7, 1;
1, -8, -15, -20, -23, -24, -23, -20, -15, -8, 1;
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MAPLE
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1+m*(m-n) ;
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MATHEMATICA
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Table[k*(k-n)+1, {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 30 2019 *)
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PROG
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(Magma) [[k*(k-n)+1: k in [0..n]]: n in [0..12]]; // G. C. Greubel, May 30 2019
(Sage) [[k*(k-n)+1 for k in (0..n)] for n in (0..12)] # G. C. Greubel, May 30 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> k*(k-n)+1 ))); # G. C. Greubel, May 30 2019
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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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