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Search: id:A094430
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| A094430 |
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a(n) = rightmost term of M^n * [1 0 0], M = the 3 X 3 matrix [0 1 0 / 0 0 1 / 7 -14 7] M^n |
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+0
2
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| 7, 49, 245, 1078, 4459, 17836, 69972, 271313, 1044435, 4002467, 15294370, 58337097, 222255768, 846131608, 3219700183, 12247849145, 46582062709, 177142452214, 673583231587, 2561162729076, 9737971026812, 37024601601729
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OFFSET
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1,1
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COMMENT
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In A094429 the multiplier is [1 1 1] instead of [1 0 0]. The matrix M is derived from the 3rd order Lucas polynomial x^3 - 7x^2 + 14x - 7, with a convergent of the series = 3.801937735...= (2 Sin 3Pi/7)^2; (an eigenvalue of the matrix and a root of the polynomial).
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EXAMPLE
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a(4) = 1078 since M^4 * [1 0 0] = [49 245 1078] = [a(2), a(3), a(4)].
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MATHEMATICA
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Table[(MatrixPower[{{0, 1, 0}, {0, 0, 1}, {7, -14, 7}}, n].{1, 0, 0})[[3]], {n, 22}] (from Robert G. Wilson v)
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CROSSREFS
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Cf. A094429.
Sequence in context: A003530 A015953 A133047 this_sequence A113235 A133046 A126639
Adjacent sequences: A094427 A094428 A094429 this_sequence A094431 A094432 A094433
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 02 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 08 2004
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