OFFSET
0,7
COMMENTS
Row sums are A164586.
FORMULA
T(n,k) = T(n-1,k-1)+T(n-2,k-1)+T(n-3,k)+T(n-2,k+1)+T(n-1,k+1); T(n,n) = 1.
Riordan array ((1/(1-x^3))*c((x(1+x)/(1-x^3))^2), (x(1+x)/(1-x^3))*c((x(1+x)/(1-x^3))^2)), c(x) the g.f. of A000108.
EXAMPLE
Triangle begins
1,
0, 1,
1, 1, 1,
3, 2, 2, 1,
3, 8, 4, 3, 1,
11, 13, 15, 7, 4, 1,
24, 35, 33, 25, 11, 5, 1,
51, 91, 84, 66, 39, 16, 6, 1,
137, 205, 232, 174, 116, 58, 22, 7, 1,
320, 539, 569, 496, 325, 188, 83, 29, 8, 1
MAPLE
A164585 := proc(n, k)
option remember;
if k < 0 or k> n or n < 0 then
0;
elif k = n then
1 ;
else
procname(n-1, k-1)
+procname(n-2, k-1)
+procname(n-3, k)
+procname(n-2, k+1)
+procname(n-1, k+1) ;
end if;
end proc:
seq(seq(A164585(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Feb 10 2015
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Aug 17 2009
STATUS
approved