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A114225 A Pascal-Thue-Morse triangle. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified April 13 12:29 EDT 2021. Contains 342936 sequences. (Running on oeis4.)