A113678 Sequence array for A078008.

1, 0, 1, 2, 0, 1, 2, 2, 0, 1, 6, 2, 2, 0, 1, 10, 6, 2, 2, 0, 1, 22, 10, 6, 2, 2, 0, 1, 42, 22, 10, 6, 2, 2, 0, 1, 86, 42, 22, 10, 6, 2, 2, 0, 1, 170, 86, 42, 22, 10, 6, 2, 2, 0, 1, 342, 170, 86, 42, 22, 10, 6, 2, 2, 0, 1, 682, 342, 170, 86, 42, 22, 10, 6, 2, 2, 0, 1, 1366, 682, 342, 170, 86

Offset: 0

Author

Paul Barry, Nov 04 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A001045(n+1). Diagonal sums are A053088. Inverse is A113680.

Examples

			Triangle begins
1;
0, 1;
2, 0, 1;
2, 2, 0, 1;
6, 2, 2, 0, 1;
10, 6, 2, 2, 0, 1;
22, 10, 6, 2, 2, 0, 1;
		

Formula

Riordan array ((1-x)/(1-x-2x^2), x); Number triangle T(n, k)=if(k<=n, (2^(n-k)+2(-1)^(n-k))/3, 0); T(n, k)=sum{i=0..n, C(n-i, k)C(k, n-i)(2^i+2(-1)^i)/3}.