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A114225 A Pascal-Thue-Morse triangle. 1

%I

%S 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,

%T 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,

%U 57,105,126,105,57,17,10,1

%N A Pascal-Thue-Morse triangle.

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

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

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

%F 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).

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

%F 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)}.

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

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 3, 3, 1;

%e 1, 4, 5, 4, 1;

%e 1, 5, 7, 7, 5, 1;

%e 1, 6, 9,11, 9, 6, 1;

%e 1, 7,11,17,17,11, 7; 1;

%e 1, 8,13,26,33,26,13, 8, 1;

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Nov 18 2005

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Last modified June 19 12:49 EDT 2021. Contains 345129 sequences. (Running on oeis4.)