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A162516
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Triangle of coefficients of polynomials defined by Binet form: P(n,x) = (U^n+L^n)/2, where U=x+d, L=x-d, d=(x+4)^(1/2).
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4
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1, 1, 0, 1, 1, 4, 1, 3, 12, 0, 1, 6, 25, 8, 16, 1, 10, 45, 40, 80, 0, 1, 15, 75, 121, 252, 48, 64, 1, 21, 119, 287, 644, 336, 448, 0, 1, 28, 182, 588, 1457, 1360, 1888, 256, 256, 1, 36, 270, 1092, 3033, 4176, 6240, 2304, 2304, 0, 1, 45, 390, 1890, 5925, 10801, 17780
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| For fixed k, the sequences P(n,k), for n=1,2,3,4,5, are
A084057, A084059, A146963, A081342, A081342, respectively.
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FORMULA
| P(n,x)=2x*P(n-1,x)-(x^2-x-4)*P(n-2,x).
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EXAMPLE
| First six rows:
1
1...0
1...1...4
1...3...12...0
1...6...25...8...16
1...10..48...40..80...0
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CROSSREFS
| A162514, A162515, A162517.
Sequence in context: A154182 A093735 A156224 * A193793 A085471 A064221
Adjacent sequences: A162513 A162514 A162515 * A162517 A162518 A162519
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 05 2009
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