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Search: id:A158982
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| A158982 |
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Coefficients of polynomials P(n,x):=-2+P(n-1,x)^2, where P(0,x)=x-2. |
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5
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| 1, -2, 1, -4, 2, 1, -8, 20, -16, 2, 1, -16, 104, -352, 660, -672, 336, -64, 2, 1, -32, 464, -4032, 23400, -95680, 283360, -615296, 980628, -1136960, 940576, -537472, 201552, -45696, 5440, -256, 2, 1, -64, 1952, -37760, 520144, -5430656, 44662464
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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(1) The 2^n zeros of P(n,x) are 2+2*cos[(2k-1)pi/(2^(n+2))], k=1,2,...,2^n.
(2) P(n,x)=2*T(2^(n+1),(1/2)x^(1/2)), where T(k,t) is the kth Chebyshev
polynomial of the first kind.
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REFERENCES
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Clark Kimberling, "Polynomials defined by the recurrence P(n+1)=(P(n)+c-a)^2 - c," preprint, 2009.
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FORMULA
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P(n+1,x+2)=P(n,x^2) for n>=0.
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EXAMPLE
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Row 1: 1 -2 (from x-2)
Row 2: 1 -4 2 (from x^2-4x+2)
Row 3: 1 -8 20 -16 2
Row 4: 1 -16 104 -352 660 -672 336 -64 2
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CROSSREFS
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A084534, A158983, A158984, A158985, A158986.
Sequence in context: A060637 A123486 A158264 this_sequence A127124 A127136 A145983
Adjacent sequences: A158979 A158980 A158981 this_sequence A158983 A158984 A158985
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KEYWORD
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sign,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Apr 02 2009
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