A114225 A Pascal-Thue-Morse triangle.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 5, 7, 7, 5, 1, 1, 6, 9, 11, 9, 6, 1, 1, 7, 11, 17, 17, 11, 7, 1, 1, 8, 13, 26, 33, 26, 13, 8, 1, 1, 9, 15, 39, 61, 61, 39, 15, 9, 1, 1, 10, 17, 57, 105, 126, 105, 57, 17, 10, 1

Offset

0,5

Comments

Row sums are A114226. Inverse has row sums 0^n.

Links

Table of n, a(n) for n=0..65.

Formula

As a number triangle, T(n, k) = sum{j=0..n-k, C(n-k, j)*C(k, j)*A010060(j+1)}.

As a number triangle, T(n, k) = sum{j=0..n, C(n-k, n-j)*C(k, j-k)*A010060(j-k+1)}.

As a number triangle, T(n, k) = if(k<=n, sum{j=0..n, C(k, j)*C(n-k, n-j)*A010060(k-j+1)}, 0).

As a square array, T(n, k) = sum{j=0..n, C(n, j)*C(k, j)*A010060(j+1)}.

As a square array, T(n, k) = sum{j=0..n+k, C(n, n+k-j)*C(k, j-k)*A010060(j-k+1)}.

Column k has g.f. sum{j=0..k, C(k, j)A010060(j+1)(x/(1-x))^j}x^k/(1-x).

Example

1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 5, 4, 1;
1, 5, 7, 7, 5, 1;
1, 6, 9,11, 9, 6, 1;
1, 7,11,17,17,11, 7; 1;
1, 8,13,26,33,26,13, 8, 1;

Crossrefs

Sequence in context: A132892 A174448 A077028 * A193515 A259874 A256141

Adjacent sequences: A114222 A114223 A114224 * A114226 A114227 A114228

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 18 2005

Status

approved