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Search: id:A114225
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| A114225 |
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A Pascal-Thue-Morse triangle. |
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+0
2
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| 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; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A114226. Inverse has row sums 0^n.
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FORMULA
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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);
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EXAMPLE
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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;
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CROSSREFS
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Sequence in context: A107430 A132892 A077028 this_sequence A072704 A038792 A046688
Adjacent sequences: A114222 A114223 A114224 this_sequence A114226 A114227 A114228
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 18 2005
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