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A176625
T(n,k) = 1 + 3*k*(k - n), triangle read by rows (n >= 0, 0 <= k <= n).
2
1, 1, 1, 1, -2, 1, 1, -5, -5, 1, 1, -8, -11, -8, 1, 1, -11, -17, -17, -11, 1, 1, -14, -23, -26, -23, -14, 1, 1, -17, -29, -35, -35, -29, -17, 1, 1, -20, -35, -44, -47, -44, -35, -20, 1, 1, -23, -41, -53, -59, -59, -53, -41, -23, 1, 1, -26, -47, -62, -71, -74, -71, -62, -47
OFFSET
0,5
FORMULA
T(n,k) = 1 - A000326(n) + A000326(k) + A000326(n-k).
EXAMPLE
Triangle begins:
1;
1, 1;
1, -2, 1:
1, -5, -5, 1;
1, -8, -11, -8, 1;
1, -11, -17, -17, -11, 1;
1, -14, -23, -26, -23, -14, 1;
1, -17, -29, -35, -35, -29, -17, 1;
1, -20, -35, -44, -47, -44, -35, -20, 1;
1, -23, -41, -53, -59, -59, -53, -41, -23, 1;
1, -26, -47, -62, -71, -74, -71, -62, -47, -26, 1;
...
MATHEMATICA
a[n_] = n*(3*n - 1)/2; (* A000326 *)
t[n_, m_] = 1 - a[n] + a[m] + a[n - m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
PROG
(Maxima) create_list(1 + 3*k*(k - n), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Nov 25 2018 */
(Magma) / * As triangle */ [[1 + 3*k*(k - n): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Nov 26 2018
KEYWORD
sign,tabl,easy
AUTHOR
Roger L. Bagula, Apr 22 2010
EXTENSIONS
Edited and name clarified by Franck Maminirina Ramaharo, Nov 25 2018
STATUS
approved