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%I #13 Oct 19 2022 10:59:35
%S 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,
%T 118,153,125,70,27,7,1,81,244,359,336,220,104,35,8,1,149,499,819,864,
%U 646,357,147,44,9,1,274,1010,1830,2144,1800,1134,546,200,54,10,1,504
%N Tribonacci convolution triangle.
%C First column is A000073(n+2). Row sums are A077939. Diagonal sums are A002478.
%F Riordan array (1/(1-x-x^2-x^3), x/(1-x-x^2-x^3))
%F Contribution from _Paul Barry_, Jun 02 2009: (Start)
%F 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)
%F for n >= 0 and 0< = m< = n and T'(n, m) = 0 otherwise. (End)
%F 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]
%e Rows begin {1},{1,1},{2,2,1},{4,5,3,1},{7,12,9,4,1},...
%p # Uses function PMatrix from A357368. Adds column 1,0,0,0,... to the left.
%p PMatrix(10, n -> A000073(n+1)); # _Peter Luschny_, Oct 19 2022
%o (Maxima) trinomial(n,k):=coeff(expand((1+x+x^2)^n),x,k);
%o 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]
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Mar 16 2005
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