A112906 A skew generalized Pascal triangle.

1, 0, 3, 0, 1, 10, 0, 0, 6, 33, 0, 0, 1, 29, 109, 0, 0, 0, 9, 126, 360, 0, 0, 0, 1, 57, 516, 1189, 0, 0, 0, 0, 12, 306, 2034, 3927, 0, 0, 0, 0, 1, 94, 1491, 7807, 12970, 0, 0, 0, 0, 0, 15, 600, 6813, 29382, 42837, 0, 0, 0, 0, 0, 1, 140, 3385, 29737, 108923, 141481, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, Oct 05 2005

Keywords

• easy
• nonn
• tabl

Comments

Main diagonal is A006190. Row sums are A007482. Column sums are A001076(n+1). Compare with [0,1/3,-1/3,0,0,..] DELTA [3,1/3,-1/3,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-3x-x^2),x/(1-3x-x^2)).

Examples

			Triangle begins
1;
0, 3;
0, 1, 10;
0, 0, 6, 33;
0, 0, 1, 29, 109;
0, 0, 0, 9, 126, 360,
0, 0, 0, 1, 57, 516, 1189;
0, 0, 0, 0, 12, 306, 2034, 3927;
0, 0, 0, 0, 1, 94, 1491, 7809, 12970;
		

Crossrefs

Cf. A112899.

Formula

G.f.: 1/(1-3xy(1+x/3)-x^2*y^2); T(n, k)=sum{j=0..floor((2k-n)/2), C(k-j, n-k)C(2k-n, j)3^(2k-2j-n)}; T(n, k) = 3*T(n-1, k-1)+T(n-2, k-1)+T(n-2, k-2).