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Search: id:A136688
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| A136688 |
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Triangular sequence of q-Fibonacci polynomials for s=2: 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, 2, 0, 1, 0, 4, 0, 1, 4, 0, 6, 0, 1, 0, 12, 0, 8, 0, 1, 8, 0, 24, 0, 10, 0, 1, 0, 32, 0, 40, 0, 12, 0, 1, 16, 0, 80, 0, 60, 0, 14, 0, 1, 0, 80, 0, 160, 0, 84, 0, 16, 0, 1, 32, 0, 240, 0, 280, 0, 112, 0, 18, 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, 3, 5, 11, 21, 43, 85, 171, 341, 683};
Riordan array (1/(1-2x^2),x/(1-2x^2)). - Paul Barry (pbarry(AT)wit.ie), Jun 18 2008
Diagonal sums are 1,0,3,0,9,... with g.f. 1/(1-3x^2). - Paul Barry (pbarry(AT)wit.ie), Jun 18 2008
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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=2: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},
{2, 0, 1},
{0, 4, 0, 1},
{4, 0, 6, 0, 1},
{0, 12, 0, 8, 0, 1},
{8, 0, 24, 0, 10, 0, 1},
{0, 32, 0, 40, 0, 12, 0, 1},
{16, 0, 80, 0, 60, 0, 14, 0, 1},
{0, 80, 0, 160, 0, 84, 0, 16, 0, 1},
{32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1}
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MATHEMATICA
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Clear[F, x, s, n] s = 2; 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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Sequence in context: A143782 A073430 A053389 this_sequence A131321 A111959 A110109
Adjacent sequences: A136685 A136686 A136687 this_sequence A136689 A136690 A136691
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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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