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Search: id:A103141
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| A103141 |
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Riordan array (1/(1-x), x(1+x+x^2+x^3)/(1-x)). |
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+0
2
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| 1, 1, 1, 1, 3, 1, 1, 6, 5, 1, 1, 10, 15, 7, 1, 1, 14, 35, 28, 9, 1, 1, 18, 68, 84, 45, 11, 1, 1, 22, 116, 207, 165, 66, 13, 1, 1, 26, 180, 441, 491, 286, 91, 15, 1, 1, 30, 260, 840, 1251, 996, 455, 120, 17, 1, 1, 34, 356, 1464, 2823, 2948, 1814, 680, 153, 19, 1, 1, 38, 468, 2376
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Generalized Pascal matrix : row sums are generalized Pell numbers A103142 and diagonal sums are the Pentanacci numbers A001591(n+4). One of a family of generalized Pascal triangles given by the Riordan arrays (1/(1-x), x*sum{j=0..k, x^k}/(1-x)). This array has the 'k+2-nacci' numbers as diagonal sums and generalized Pell numbers a(n)=2a(n-1)+sum{j=1..k, a(n-1-j} as row sums. The first two arrays of the family are Pascal's triangle and the Delannoy number triangle.
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FORMULA
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Triangle, read by rows, where the terms are generated by the rule: T(n, k) = T(n-1, k) + T(n-1, k-1) + T(n-2, k-1) + T(n-3, k-1)+T(n-4, k-1), with T(0, 0)=1.
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EXAMPLE
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Rows begin {1}, {1,1}, {1,3,1}, {1,6,5,1}, {1,10,15,7,1},...
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CROSSREFS
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Cf. A102036.
Sequence in context: A124802 A102036 A121524 this_sequence A085478 A123970 A129818
Adjacent sequences: A103138 A103139 A103140 this_sequence A103142 A103143 A103144
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 24 2005
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