A124369 Riordan array (1/((1-x-x^2)(1+x+x^2)),x(1+x)/((1-x-x^2)(1+x+x^2))).

1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 6, 4, 3, 1, 4, 9, 12, 7, 4, 1, 7, 17, 24, 21, 11, 5, 1, 10, 34, 48, 50, 34, 16, 6, 1, 17, 58, 103, 110, 91, 52, 22, 7, 1, 28, 104, 200, 250, 220, 152, 76, 29, 8, 1, 44, 188, 385, 534, 530, 400, 239, 107, 37, 9, 1

Offset: 0

Author

Paul Barry, Oct 27 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A123392. Diagonal sums are A124370. First column is A094686. Product of A026729 and abs(A049310).

Examples

			Triangle begins
1,
0, 1,
1, 1, 1,
2, 2, 2, 1,
2, 6, 4, 3, 1,
4, 9, 12, 7, 4, 1,
7, 17, 24, 21, 11, 5, 1,
10, 34, 48, 50, 34, 16, 6, 1,
17, 58, 103, 110, 91, 52, 22, 7, 1
		

Formula

Number triangle T(n,k)=sum{j=0..n, C(j,n-j)*C((j+k)/2,(j-k)/2)*(1+(-1)^(j-k))/2};

T(n,k) = T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + 2*T(n-3,k) + T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 22 2014