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A104580 Tribonacci convolution triangle.

%I A104580 #23 Jun 24 2025 10:41:55
%S A104580 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 A104580 118,153,125,70,27,7,1,81,244,359,336,220,104,35,8,1,149,499,819,864,
%U A104580 646,357,147,44,9,1,274,1010,1830,2144,1800,1134,546,200,54,10,1
%N A104580 Tribonacci convolution triangle.
%F A104580 Riordan array (1/(1-x-x^2-x^3), x/(1-x-x^2-x^3)).
%F A104580 From _Paul Barry_, Jun 02 2009: (Start)
%F A104580 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)
%F A104580 T(n,k) = Sum_{i=0..n-k} binomial(i+k,k)*A027907(i,n-k-i). - _Emanuele Munarini_, Mar 15 2011
%e A104580 Rows begin
%e A104580   {1},
%e A104580   {1,1},
%e A104580   {2,2,1},
%e A104580   {4,5,3,1},
%e A104580   {7,12,9,4,1},
%e A104580    ...
%p A104580 # Uses function PMatrix from A357368. Adds column 1,0,0,0,... to the left.
%p A104580 PMatrix(10, n -> A000073(n+1)); # _Peter Luschny_, Oct 19 2022
%o A104580 (Maxima) trinomial(n,k):=coeff(expand((1+x+x^2)^n),x,k);
%o A104580 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 */
%Y A104580 First column is A000073(n+2). Row sums are A077939. Diagonal sums are A002478.
%K A104580 easy,nonn,tabl
%O A104580 0,4
%A A104580 _Paul Barry_, Mar 16 2005