A026148 Irregular triangular array T read by rows: T(n,0) = 1 for i >= 0, T(1,1) = 1,T(2,1) = 1, T(2,2) = 2, T(2,3) = 1, T(2,4) = 1 and for n >= 3, T(n,1) = n-1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k=2,...,n+1, and T(n, k+2) = T(n-1, k) + T(n-1, k+1).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 4, 4, 4, 2, 1, 3, 7, 10, 12, 10, 6, 1, 4, 11, 20, 29, 32, 28, 16, 1, 5, 16, 35, 60, 81, 89, 76, 44, 1, 6, 22, 56, 111, 176, 230, 246, 209, 120, 1, 7, 29, 84, 189, 343, 517, 652, 685, 575, 329, 1, 8, 37, 120, 302, 616, 1049, 1512, 1854, 1912, 1589, 904, 1, 9, 46, 165

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabf

Examples

			First 7 rows:
  1
  1  1
  1  1  2  1  1
  1  2  4  4  4  2
  1  3  7 10 12 10  6
  1  4 11 20 29 32 28 16
  1  5 16 35 60 81 89 76 44
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..5000

Programs

Mathematica

z = 12; t[n_, 0] = 1; t[1, 1] = 1; t[2, 2] = 2; t[2, 3] = 1; t[2, 4] = 1; t[n_, 1] := t[n, 1] = n - 1; t[n_, k_] := t[n, k] = Which[2 <= k <= n + 1, t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k], k == n + 2, t[n - 1, k - 2] + t[n - 1, k - 1]]; u = Join[{{1}}, {{1, 1}}, Table[t[n, k], {n, 2, z}, {k, 0, n + 2}]]; TableForm[u] (* A026148 array *)
Flatten[u] (* A026148 sequence *) (*  Clark Kimberling, Aug 28 2014 *)

Extensions

Definition clarified and Example by Clark Kimberling, Aug 28 2014