A383609 Triangle read by rows: T(n,k) = T(n-1, k-2) + T(n-1, k-1) + T(n-1, k) for 0 < k < n, T(n,0) = T(n,n) = 1.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 8, 8, 1, 1, 5, 13, 20, 17, 1, 1, 6, 19, 38, 50, 38, 1, 1, 7, 26, 63, 107, 126, 89, 1, 1, 8, 34, 96, 196, 296, 322, 216, 1, 1, 9, 43, 138, 326, 588, 814, 834, 539, 1, 1, 10, 53, 190, 507, 1052, 1728, 2236, 2187, 1374, 1

Offset: 0

Author

Mélika Tebni, May 02 2025

Keywords

• nonn
• tabl

Examples

			Triangle T(n, k) starts:
n\k :     0       1       2        3        4       5       6       7
 ====================================================================
  0 :     1
  1 :     1       1
  2 :     1       2       1
  3 :     1       3       4        1
  4 :     1       4       8        8        1
  5 :     1       5      13       20       17       1
  6 :     1       6      19       38       50      38       1
  7 :     1       7      26       63      107     126      89      1
  ...
		

Crossrefs

Cf. A038185, A167630, A211278.

Programs

Maple

T := proc (n, k) option remember; if k = n or k = 0 then 1 elif k < 0 then 0 else T(n-1, k-2)+T(n-1, k-1)+T(n-1, k) end if end proc:
seq(print(seq(T(n, k), k = 0 .. n)), n = 0 .. 8);

Formula

Sum_{k=0..n} 2^(n-k)*(T(n, k)(mod 2)) = A038185(n).

Sum_{j=0..n}(Sum_{k=0..j} T(j, k)) = A211278(n).

T(n,k) = A167630(n,n-k).