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Search: id:A099557
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| A099557 |
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Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n-[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x). |
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+0
3
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| 1, 1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 4, 3, 1, 0, 1, 5, 6, 4, 0, 0, 1, 6, 10, 10, 1, 0, 0, 1, 7, 15, 20, 5, 1, 0, 0, 1, 8, 21, 35, 15, 6, 0, 0, 0, 1, 9, 28, 56, 35, 21, 1, 0, 0, 0, 1, 10, 36, 84, 70, 56, 7, 1, 0, 0, 0, 1, 11, 45, 120, 126, 126, 28, 8, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums form A005314. Antidiagonal sums form A099558.
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FORMULA
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G.f.: (1-x+x*y)/((1-x)^2-x^3*y^2).
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EXAMPLE
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Rows begin:
[1],
[1,1],
[1,2,0],
[1,3,1,0],
[1,4,3,1,0],
[1,5,6,4,0,0],
[1,6,10,10,1,0,0],
[1,7,15,20,5,1,0,0],
[1,8,21,35,15,6,0,0,0],
[1,9,28,56,35,21,1,0,0,0],
[1,10,36,84,70,56,7,1,0,0,0],...
and can be derived from Pascal's triangle
by shifting each column k down by [k/2] rows.
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PROGRAM
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(PARI) {T(n, k)=polcoeff(polcoeff((1-x+x*y)/((1-x)^2-x^3*y^2)+x*O(x^n), n, x)+y*O(y^k), k, y)}
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CROSSREFS
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Cf. A005314, A099558.
Sequence in context: A089994 A100260 A124943 this_sequence A079217 A079221 A026794
Adjacent sequences: A099554 A099555 A099556 this_sequence A099558 A099559 A099560
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 22 2004
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