OFFSET
0,4
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
KEYWORD
AUTHOR
Paul Barry, Mar 16 2005
STATUS
approved