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Search: id:A124216
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| A124216 |
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Generalized Pascal triangle. |
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+0
2
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| 1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 34, 16, 1, 1, 25, 90, 90, 25, 1, 1, 36, 195, 328, 195, 36, 1, 1, 49, 371, 931, 931, 371, 49, 1, 1, 64, 644, 2240, 3334, 2240, 644, 64, 1, 1, 81, 1044, 4788, 9846, 9846
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Consider the 1-parameter family of triangles with g.f. (1-x(1+y))/(1-2x(1+y)+x^2(1+k*x+y^2)). A007318 corresponds to k=2. A056241 corresponds to k=1. A124216 corresponds to k=0. Row sums are A006012. Diagonal sums are A124217.
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FORMULA
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G.f.: (1-x(1+y))/(1-2x(1+y)+x^2(1+y^2)); Number triangle T(n,k)=sum{j=0..n, C(n,j)C(j,2(j-k))2^(j-k)}.
Equals 2*A001263 - A007318; (i.e. twice the Narayana triangle minus Pascal's triangle). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2007
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EXAMPLE
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Triangle begins
1,
1, 1,
1, 4, 1,
1, 9, 9, 1,
1, 16, 34, 16, 1,
1, 25, 90, 90, 25, 1,
1, 36, 195, 328, 195, 36, 1,
1, 49, 371, 931, 931, 371, 49, 1
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CROSSREFS
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Cf. A001263.
Sequence in context: A082950 A060102 A082043 this_sequence A008459 A039756 A126065
Adjacent sequences: A124213 A124214 A124215 this_sequence A124217 A124218 A124219
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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), Oct 19 2006
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