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

0,2

Comments

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

Links

Table of n, a(n) for n=0..63.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A004070.

Sequence in context: A101559 A220537 A229717 * A350122 A156708 A131250

Adjacent sequences: A122435 A122436 A122437 * A122439 A122440 A122441

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 05 2006

Extensions

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

Status

approved