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A373746
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Triangle read by rows: the almost-Riordan array ( 1/(1-x) | 2/((1-x)*(1+x+sqrt(5*x^2-6*x+1))), (1-3*x-sqrt(5*x^2-6*x+1))/(2x) ).
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0
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1, 1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 10, 20, 8, 1, 1, 31, 78, 45, 11, 1, 1, 110, 310, 224, 79, 14, 1, 1, 421, 1264, 1061, 475, 122, 17, 1, 1, 1686, 5274, 4922, 2608, 858, 174, 20, 1, 1, 6961, 22430, 22648, 13604, 5356, 1400, 235, 23, 1, 1, 29392, 96899, 103978, 68816, 31072, 9791, 2128, 305, 26, 1
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OFFSET
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0,5
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COMMENTS
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In He and Słowik, there is a typing error since T(5,1) is equal to 31 and not to 421.
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LINKS
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FORMULA
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EXAMPLE
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The triangle begins as:
1;
1, 1;
1, 2, 1;
1, 4, 5, 1;
1, 10, 20, 8, 1;
1, 31, 78, 45, 11, 1;
1, 110, 310, 224, 79, 14, 1;
...
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MATHEMATICA
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T[n_, 0]:=1; T[n_, k_]:=SeriesCoefficient[2/((1-x)(1+x+Sqrt[5x^2-6x+1]))((1-3x-Sqrt[5x^2-6x+1])/(2x))^(k-1), {x, 0, n-1}]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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