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A094253
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Let M = the 3 X 3 Matrix [ -4 4 8 / 1 0 0 / 0 1 0]. Then a(n) = absolute value of the center term of M^n * [1 1 1].
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1, 8, 20, 120, 496, 2304, 10240, 46208, 207360, 932352, 4189184, 18827264, 84606976, 380223488, 1708703744, 7678853120, 34508439552, 155079540736, 696921096192, 3131935031296, 14074788184064, 63251524091904
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The matrix is derived from the polynomial 8x^3 + 4x^2 - 4x - 1 shown on page 204 of "Advanced Trigonometry". Cos 2Pi/7, Cos 4Pi/7, Cos 6Pi/7 are roots of this polynomial.
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REFERENCES
| C. V. Durell & A. Robson, "Advanced Trigonometry", Dover 2003, p. 204.
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FORMULA
| 2. a(n)/a(n-1) tends to 1/Cos 3Pi/7 = 4.4939592074...; e.g. a(10)/a(9) = 932352/207360 = 4.4962962...
a(n)=4*a(n-1)+4*a(n-2)-8*a(n-3), n>4. G.f.: x*(1+4*x-16*x^2+16*x^3)/(1-4*x-4*x^2+8*x^3). [Colin Barker, Feb 01 2012]
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EXAMPLE
| a(3) = 20 since M^3 * [1 1 1 ] = [120 -20 8]. Take the absolute value of the center term.
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MATHEMATICA
| Table[ Abs[ MatrixPower[{{-4, 4, 8}, {1, 0, 0}, {0, 1, 0}}, n].{1, 1, 1}][[2]], {n, 23}] (from Robert G. Wilson v Apr 28 2004)
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CROSSREFS
| Sequence in context: A014584 A074472 A175429 * A060668 A079386 A108235
Adjacent sequences: A094250 A094251 A094252 * A094254 A094255 A094256
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 25 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 28 2004
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