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Search: id:A162517
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| A162517 |
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Triangle of coefficients of polynomials defined by Binet form: P(n,x) = (U^n-L^n)/(2d), where U=x+d, L=x-d, d=(x+4)^(1/2). |
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+0
5
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| 0, 1, 2, 0, 3, 1, 4, 4, 4, 16, 0, 5, 10, 41, 8, 16, 6, 20, 86, 48, 96, 0, 7, 35, 161, 169, 348, 48, 64, 8, 56, 280, 456, 992, 384, 512, 0, 9, 84, 462, 1044, 2449, 1744, 2400, 256, 256, 10, 120, 732, 2136, 5482, 5920, 8640, 2560, 2560, 0, 11, 165, 1122, 4026, 11407
(list; table; graph; listen)
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OFFSET
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1,3
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FORMULA
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P(n,x)=2x*P(n-1,x)-(x^2-x-4)*P(n-2,x).
Let Q(n,x) be the nth polynomial at A162516; then
Q(n,x)=P(n+1,x)-x*P(n,x).
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EXAMPLE
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First six rows:
0
1
2...0
3...1...4
4...4...16...0
5...10..41...8...16
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CROSSREFS
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A162514, A162515, A162516.
Sequence in context: A008720 A008734 A053445 this_sequence A162170 A008798 A005290
Adjacent sequences: A162514 A162515 A162516 this_sequence A162518 A162519 A162520
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 05 2009
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