A259074 Triangle T(n,k) = Sum_{j=0..(n-k)/3} C(n-3*j-1,k-1)*C(n-k-3*j,j).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 2, 4, 6, 4, 1, 3, 7, 10, 10, 5, 1, 4, 12, 18, 20, 15, 6, 1, 5, 19, 33, 39, 35, 21, 7, 1, 7, 28, 58, 76, 75, 56, 28, 8, 1, 10, 42, 96, 144, 156, 132, 84, 36, 9, 1, 14, 64, 156, 260, 315, 294, 217, 120, 45, 10, 1, 19, 97, 253, 455, 610, 630, 518, 338, 165, 55, 11, 1

Offset: 1

Author

Vladimir Kruchinin, Jun 18 2015

Keywords

• nonn
• tabl

Examples

			[1]
[1,1]
[1,2,1]
[1,3,3,1]
[2,4,6,4,1]
[3,7,10,10,5,1]
		

Crossrefs

Column k=1 gives A003269, column k=2 A292324.

Row sums give A008999(n-1) for n>0.

Programs

Mathematica

Table[Sum[Binomial[n - 3*j - 1, k - 1] Binomial[n - k - 3*j, j], {j, 0, (n - k)/3}], {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Jun 19 2015 *)

Maxima

T(n,k):=sum(binomial(n-3*j-1,k-1)*binomial(n-k-3*j,j),j,0,(n-k)/3);

Formula

G.f.: (x*y)/(1-x-x^4-x*y).