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Search: id:A136689
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| A136689 |
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Triangular sequence of q-Fibonacci polynomials for s=3: F(x,n)=x*F(x,n-1)+s*F(x,n-2). |
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1
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| 1, 0, 1, 3, 0, 1, 0, 6, 0, 1, 9, 0, 9, 0, 1, 0, 27, 0, 12, 0, 1, 27, 0, 54, 0, 15, 0, 1, 0, 108, 0, 90, 0, 18, 0, 1, 81, 0, 270, 0, 135, 0, 21, 0, 1, 0, 405, 0, 540, 0, 189, 0, 24, 0, 1, 243, 0, 1215, 0, 945, 0, 252, 0, 27, 0, 1
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums are:
{1, 1, 4, 7, 19, 40, 97, 217, 508, 1159, 2683}.
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REFERENCES
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J. Cigler, q-Fibonacci polynomials, Fibonacci Quarterly, 2003; http://homepage.univie.ac.at/johann.cigler/downloads/FIBQUART.pdf
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FORMULA
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s=3:F(x,0)=0;F(x,1)=1; F(x,n)=x*F(x,n-1)+s*F(x,n-2)
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EXAMPLE
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{1},
{0, 1},
{3, 0, 1},
{0, 6, 0, 1},
{9, 0, 9, 0, 1},
{0, 27, 0, 12, 0, 1},
{27, 0, 54, 0, 15, 0, 1},
{0, 108, 0, 90, 0, 18, 0, 1},
{81, 0, 270, 0, 135,0, 21, 0, 1},
{0, 405, 0, 540, 0, 189, 0, 24, 0, 1},
{243, 0, 1215, 0, 945, 0, 252, 0, 27, 0, 1}
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MATHEMATICA
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Clear[F, x, s, n] s = 3; F[x, 0] = 0; F[x, 1] = 1; F[x_, n_] := F[x, n] = x*F[x, n - 1] + s*F[x, n - 2]; Table[ExpandAll[F[x, n]], {n, 1, 11}]; a = Table[CoefficientList[F[x, n], x], {n, 1, 11}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A136686 A136687 A136688 this_sequence A136690 A136691 A136692
Sequence in context: A100574 A056100 A141665 this_sequence A073278 A135481 A128311
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 06 2008
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