OFFSET
0,5
COMMENTS
FORMULA
Number triangle T(n, k) = binomial(n+2k, 3k).
T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k) + T(n-1,k-1). - Philippe Deléham, Feb 18 2012
G.f.: (1-x)^2/((1-x)^3-y*x). - Philippe Deléham, Feb 18 2012
Sum_{k, 0<=k<=n} T(n,k)*x^k = A185963(n), A000012(n), A052544(n), A049086(n) for x = -1, 0, 1, 2 respectively. - Philippe Deléham, Feb 18 2012
EXAMPLE
Rows begin
1;
1,1;
1,4,1;
1,10,7,1;
1,20,28,10,1;
1,35,84,55,13,1;
PROG
(PARI) tabl(nn) = {my(m = matrix(nn, nn, n, k, if (n<k, 0, binomial(n+2*k-3, 3*k-3)))); for (n=1, nn, for (k=1, n, print1(m[n, k], ", "); ); print(); ); } \\ Michel Marcus, Nov 20 2015
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jul 06 2005
STATUS
approved