A176625 T(n,k) = 1 + 3*k*(k - n), triangle read by rows (n >= 0, 0 <= k <= n).

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

Author

Roger L. Bagula, Apr 22 2010

Keywords

• sign
• tabl
• easy

Examples

			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;
  ...
		

Crossrefs

Cf. A000326, A156070, A156072, A176305, A176306, A176307, A176339, A176344.

Programs

Magma

/ * As triangle */ [[1 + 3*k*(k - n): k in [0..n]]: n in [0.. 15]];  // Vincenzo Librandi, Nov 26 2018

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[%]

Maxima

create_list(1 + 3*k*(k - n), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Nov 25 2018 */

Formula

T(n,k) = 1 - A000326(n) + A000326(k) + A000326(n-k).

Extensions

Edited and name clarified by Franck Maminirina Ramaharo, Nov 25 2018