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A094434
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a(n) = rightmost term of M^n * [1 0 0], with M = the 3 X 3 matrix [1 -1 0 / -1 3 -2 / 0 -2 2].
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1
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0, 2, 12, 60, 288, 1368, 6480, 30672, 145152, 686880, 3250368, 15380928, 72783360, 344414592, 1629787392, 7712236800, 36494696448, 172694757888, 817200368640, 3867033664512, 18298999775232, 86591796664320, 409756781334528
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Left term in M^n * [1 0 0] = A094433(n). a(n)/ a(n-1) tends to 3 + sqrt(3) = 4.732050807...; e.g. a(9)/a(8) = 145152/30672 = 4.732394... 3. a(n)/ A094433(n) tends to 1 + sqrt(3); e.g. a(9)/A094433(9) = 145152/53136 = 2.731707... 4. M = a "stiffness matrix" with k1 = 1, k2 = 2, relating to Hooke's law governing the force on the nodes of compressed or stretched springs with stiffness constants k1, k2. (see A094433, A094431).
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REFERENCES
| Carl D. Meyer, "Matrix Analysis and Applied Linear Algebra", SIAM, 2000, p. 86-87.
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EXAMPLE
| a(4) = 60 since M^4 * [1 0 0] = [24 -84 60].
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MATHEMATICA
| Table[(MatrixPower[{{1, -1, 0}, {-1, 3, -2}, {0, -2, 2}}, n].{1, 0, 0})[[3]], {n, 24}] (from Robert G. Wilson v)
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CROSSREFS
| Cf. A094431, A094431, A094433.
Sequence in context: A143770 A062478 A005430 * A001574 A074445 A038154
Adjacent sequences: A094431 A094432 A094433 * A094435 A094436 A094437
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 02 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 08 2004
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