A156072 T(n,k) = 1 + a(n) - a(k) - a(n - k), where a(n) = A078012(n+2), triangle read by rows (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 3, 5, 6, 6, 6, 5, 3, 1, 1, 4, 7, 9, 9, 9, 9, 7, 4, 1, 1, 6, 10, 13, 14, 14, 14, 13, 10, 6, 1, 1, 9, 15, 19, 21, 22, 22, 21, 19, 15, 9, 1, 1, 13, 22, 28, 31, 33, 34, 33, 31, 28, 22, 13, 1

Offset: 0

Author

Roger L. Bagula, Feb 03 2009

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  1;
  1, 1;
  1, 0,  1;
  1, 0,  0,  1;
  1, 1,  1,  1,  1;
  1, 1,  2,  2,  1,  1;
  1, 1,  2,  3,  2,  1,  1;
  1, 2,  3,  4,  4,  3,  2,  1;
  1, 3,  5,  6,  6,  6,  5,  3,  1;
  1, 4,  7,  9,  9,  9,  9,  7,  4, 1;
  1, 6, 10, 13, 14, 14, 14, 13, 10, 6, 1;
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A000930, A156070, A176305, A176306, A176307, A176625, A176339, A176344.

Programs

Mathematica

Clear[a, t, n, m];
a[0] = 0; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 3];
t[n_, m_] := 1 + a[n] - a[m] - a[n - m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Maxima

(a[0] : 0, a[1] : 1, a[2] : 1, a[n] := a[n - 1] + a[n - 3], T(n,k) := 1 + a[n] - a[k] - a[n-k])$ create_list(T(n, k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Nov 25 2018 */

Extensions

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