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A120096
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Squares of A046717 terms.
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1
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1, 25, 169, 1681, 14641, 133225, 1194649, 10764961, 96845281, 871725625, 7845176329, 70607649841, 635465659921
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Characteristic polynomial is x^4 - 4x^3 -42x^2 - 36x + 81. a(n)/a(n-1) tends to 9. Squareroot of M = the 4 X 4 matrix: [1/u, 1, u, 1; 1, 1/u, 1, u; u, 1, 1/u, 1; 1, u, 1, 1/u]; where u, 1/u and 1 are the cyclotomic third roots of Unity: (-1, + sqrt(3)i)/2, (-1, -sqrt(3)i)/2 and 1.
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FORMULA
| Squares of A046717 terms, deleting the first "1" of A046717. a(n) = leftmost term in M^n * [1,0,0,0] where M is the 4 X 4 matrix: [1,-2,4,-2; -2,1,-2,4; 4,-2,1,-2; -2,4,-2,1].
G.f.: x(1+18x-27x^2)/((1-x)(1-9x)(1+3x)). a(n) = 7a(n-1) +21a(n-2) -27a(n-3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]
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EXAMPLE
| a(4) = 1681 = 41^2 = the square of A046717(4)
a(4) = 1681 since M^4 * [1,0,0,0] = [1681, -1640, 1600, -1640].
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CROSSREFS
| Cf. A046717.
Sequence in context: A080109 A017126 A007204 * A115330 A145964 A020250
Adjacent sequences: A120093 A120094 A120095 * A120097 A120098 A120099
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 08 2006
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