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Search: id:A117724
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| A117724 |
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Antidiagonal triangular expansion of x/(1-m*x^2+x^3): based on the A000931 sequence ( the correct Padovan/ Minimal Pisot generalized expansion). |
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1
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| 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 4, 9, 16, 25, 36, 49, 2, 4, 6, 8, 10, 12, 14, 16, 2, 9, 28, 65, 126, 217, 344, 513, 730, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300
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OFFSET
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0,12
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FORMULA
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x/(1-m^x^2+x^3)=Sum[A000931[n,m]*x^n,{n,0,Infinity}] a(n,m) = A000931[n,m]
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EXAMPLE
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0
0, 0
1, 1, 1
0, 0, 0, 0
1, 2, 3, 4, 5
1, 1, 1, 1, 1, 1
1, 4, 9, 16, 25, 36, 49
2, 4, 6, 8, 10, 12, 14, 16
2, 9, 28, 65, 126, 217, 344, 513, 730
3, 12, 27, 48, 75, 108, 147, 192, 243, 300
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MATHEMATICA
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(* define the polynomial*) p[x_] = x/(1 - m*x^2 - x^3); (* Taylor derivative expansion of the polynomial*) a = Table[Flatten[{{p[0]}, Table[Coefficient[Series[p[x], {x, 0, 30}], x^n], {n, 1, 10}]}], {m, 1, 10}] (*antidiagonal expansion to give triangular function*) b = Join[{{0}}, Delete[Table[Table[a[[ n]][[m]], {n, 1, m + 1}], {m, 0, 9}], 1]]
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CROSSREFS
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Cf. A000931.
Sequence in context: A004181 A080744 A030548 this_sequence A053841 A010884 A105932
Adjacent sequences: A117721 A117722 A117723 this_sequence A117725 A117726 A117727
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 13 2006
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