A191582 Riordan matrix (1/(1-3*x^2),x/(1-x)).

1, 0, 1, 3, 1, 1, 0, 4, 2, 1, 9, 4, 6, 3, 1, 0, 13, 10, 9, 4, 1, 27, 13, 23, 19, 13, 5, 1, 0, 40, 36, 42, 32, 18, 6, 1, 81, 40, 76, 78, 74, 50, 24, 7, 1, 0, 121, 116, 154, 152, 124, 74, 31, 8, 1, 243, 121, 237, 270, 306, 276, 198, 105, 39, 9, 1, 0, 364, 358, 507, 576, 582, 474, 303, 144, 48, 10, 1, 729, 364, 722, 865, 1083, 1158, 1056, 777, 447, 192, 58, 11, 1

Offset: 0

Author

Emanuele Munarini, Jun 07 2011

Keywords

• nonn
• easy
• tabl

Comments

Row sums = A167936(n+1).

Diagonal sums = A191584.

Central coefficients = A191585.

Alternated row sums: Sum_{k=0..n} (-1)^(n-k)*T(n,k) = 3^floor(n/2) (A167936).

Binomial row sums: Sum_{k=0..n} binomial(n,k)*T(n,k) = central coefficients.

Examples

			Triangle begins:
1
0, 1
3, 1, 1
0, 4, 2, 1
9, 4, 6, 3, 1
0, 13, 10, 9, 4, 1
27, 13, 23, 19, 13, 5, 1
0, 40, 36, 42, 32, 18, 6, 1
81, 40, 76, 78, 74, 50, 24, 7, 1
		

Crossrefs

Cf. A167936, A191584, A191585.

Programs

Mathematica

Flatten[Table[Sum[Binomial[n-2i-1,n-k-2i]3^i,{i,0,((n-k))/2}],{n,0,20},{k,0,n}]]

Maxima

create_list(sum(binomial(n-2*i-1,n-k-2*i)*3^i,i,0,(n-k)/2),n,0,20,k,0,n);

Formula

T(n,k) = Sum_{i=0..(n-k)/2} binomial(n-2*i-1,n-k-2*i)*3^i.

Recurrence: T(n+1,k+1) = T(n,k) + T(n,k+1).