OFFSET
0,4
REFERENCES
Sheng-Liang Yang et al., The Pascal rhombus and Riordan arrays, Fib. Q., 56:4 (2018), 337-347. See Fig. 4.
FORMULA
Riordan array ((1/(1-x-x^2-x^2))*c((x/(1-x-x^2-x^3))^2),(x/(1-x-x^2-x^2))*c((x/(1-x-x^2-x^3))^2)).
T(n, m) = T'(n-1, m-1)+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.
EXAMPLE
Triangle begins
1,
1, 1,
3, 2, 1,
7, 7, 3, 1,
18, 20, 12, 4, 1,
48, 59, 40, 18, 5, 1,
132, 174, 132, 68, 25, 6, 1,
372, 517, 426, 247, 105, 33, 7, 1
We have, for instance, 132=59+18+40+12+3.
MAPLE
A161009 := proc(n, m)
option remember;
if m < 0 or m >n then
0;
elif n = m then
1;
else
procname(n-1, m-1)+procname(n-1, m+1)+procname(n-1, m)+procname(n-2, m)+procname(n-3, m) ;
end if;
end proc: # R. J. Mathar, Mar 09 2016
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jun 02 2009
STATUS
approved