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A176270
Triangle T(n,m) = 1 + m*(m-n) read by rows, 0 <= m <= n.
2
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
OFFSET
0,12
COMMENTS
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
FORMULA
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).
T(n,m) = 2 - A077028(n,m) for 0 <= m <= n. - Werner Schulte, Nov 10 2020
EXAMPLE
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;
MAPLE
A176270 := proc(n, m)
1+m*(m-n) ;
end proc: # R. J. Mathar, May 03 2013
MATHEMATICA
Table[k*(k-n)+1, {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 30 2019 *)
PROG
(PARI) {T(n, k) = k*(k-n)+1}; \\ G. C. Greubel, May 30 2019
(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
CROSSREFS
Cf. A005586 (row sums), A077028.
Sequence in context: A026552 A333271 A208233 * A361802 A086437 A027907
KEYWORD
sign,tabl,easy
AUTHOR
Roger L. Bagula, Apr 13 2010
EXTENSIONS
Edited by R. J. Mathar, May 03 2013
STATUS
approved