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, 504

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..66.

Formula

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

Contribution 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(binomial(i+k,k)trinomial(i,n-k-i),i=0..n-k), where trinomial(n,k) are the trinomial coefficients (A027907) [Emanuele Munarini, Mar 15 2011]

Example

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

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

Prog

(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]

Crossrefs

Sequence in context: A355276 A272888 A001404 * A202193 A105306 A183191

Adjacent sequences: A104577 A104578 A104579 * A104581 A104582 A104583

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 16 2005

Status

approved