A104580 Tribonacci convolution triangle.

1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 7, 12, 9, 4, 1, 13, 26, 25, 14, 5, 1, 24, 56, 63, 44, 20, 6, 1, 44, 118, 153, 125, 70, 27, 7, 1, 81, 244, 359, 336, 220, 104, 35, 8, 1, 149, 499, 819, 864, 646, 357, 147, 44, 9, 1, 274, 1010, 1830, 2144, 1800, 1134, 546, 200, 54, 10, 1

Offset: 0

Author

Paul Barry, Mar 16 2005

Keywords

• easy
• nonn
• tabl

Examples

			Rows begin
  {1},
  {1,1},
  {2,2,1},
  {4,5,3,1},
  {7,12,9,4,1},
   ...
		

Crossrefs

First column is A000073(n+2). Row sums are A077939. Diagonal sums are A002478.

Programs

Maple

# Uses function PMatrix from A357368. Adds column 1,0,0,0,... to the left.
PMatrix(10, n -> A000073(n+1)); # Peter Luschny, Oct 19 2022

Maxima

trinomial(n,k):=coeff(expand((1+x+x^2)^n),x,k);
create_list(sum(binomial(i+k,k)*trinomial(i,n-k-i),i,0,n-k),n,0,8,k,0,n); /* Emanuele Munarini, Mar 15 2011 */

Formula

Riordan array (1/(1-x-x^2-x^3), x/(1-x-x^2-x^3)).

From Paul Barry, Jun 02 2009: (Start)

T(n,m) = T'(n-1,m-1) + T'(n-1,m) + T'(n-2,m) + T'(n-3,m), where T'(n,m) = T(n,m) for n >= 0 and 0 <= m <= n and T'(n,m) = 0 otherwise. (End)

T(n,k) = Sum_{i=0..n-k} binomial(i+k,k)*A027907(i,n-k-i). - Emanuele Munarini, Mar 15 2011