A122438 Riordan array (1/(1-2x), x(1+2x)).

1, 2, 1, 4, 4, 1, 8, 8, 6, 1, 16, 16, 16, 8, 1, 32, 32, 32, 28, 10, 1, 64, 64, 64, 64, 44, 12, 1, 128, 128, 128, 128, 120, 64, 14, 1, 256, 256, 256, 256, 256, 208, 88, 16, 1, 512, 512, 512, 512, 512, 496, 336, 116, 18, 1, 1024, 1024, 1024, 1024, 1024, 1024, 912, 512, 148

Offset: 0

Author

Paul Barry, Sep 05 2006

Keywords

• easy
• nonn
• tabl

Comments

Generalized Whitney triangle. Row sums are A045883(n+1). Diagonal sums are A122439.

Examples

			Number triangle begins
1,
2, 1,
4, 4, 1,
8, 8, 6, 1,
16, 16, 16, 8, 1,
32, 32, 32, 28, 10, 1,
64, 64, 64, 64, 44, 12, 1
		

Crossrefs

Cf. A004070.

Programs

Mathematica

T[n_, k_] := Sum[ Binomial[k, n - k - j]*2^(n - k), {j, 0, n - k}]; Table[ T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Robert G. Wilson v, Sep 14 2006 *)

Formula

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

Extensions

More terms from Robert G. Wilson v, Sep 14 2006