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A140184
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a(n) = 2*a(n-1) + 16*a(n-2) + 16*a(n-3).
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0
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1, 14, 60, 360, 1904, 10528, 57280, 313472, 1711872, 9355776, 51117056, 279316480, 1526198272, 8339333120, 45566902272, 248982306816, 1360464379904, 7433716105216, 40618579197952, 221944046157824, 1212724817166336, 6626451640025088, 36207605093236736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)/a(n-1) tends to (2*sqrt(3) + 2) = an eigenvalue of matrix X and a root to the characteristic polynomial x^3 - 2x^2 - 16x - 16.
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FORMULA
| a(n) - 2*a(n-1) + 16*a(n-2) + 16*a(n-3); for n>3, given a(1) = 1, a(2) = 14, a(3) = 60. Term (1,1) of X^n, where X = the 3x3 matrix [1,2,3; 2,0,2; 3,2,1].
a(n) = (2/3)*[2+2*sqrt(3)]^n*sqrt(3)+[2+2*sqrt(3)]^n+[2-2*sqrt(3)]^n-(-2)^n-(2/3)*sqrt(3) *[2-2*sqrt(3)]^n, with n>= 0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 06 2008
G.f.: x*(-1 - 12 x - 16 x^2)/(-1 + 2 x + 16 x^2 + 16 x^3) [From Harvey P. Dale, May 03 2011]
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EXAMPLE
| a(5) = 1904 = 2*a(4) + 16*a(3) + 16*a(2) = 2*360 + 16*60 + 16*14.
a(4) = 360 since term (1,1) of X^4 = 360.
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MATHEMATICA
| LinearRecurrence[{2, 16, 16}, {1, 14, 60}, 40] (* or *) CoefficientList[Series[(-1-12 x-16 x^2)/(-1+2 x+16 x^2+16 x^3), {x, 0, 40}], x] (* From Harvey P. Dale, May 03 2011 *)
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CROSSREFS
| Sequence in context: A063492 A051799 A164540 * A189948 A025415 A125849
Adjacent sequences: A140181 A140182 A140183 * A140185 A140186 A140187
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 11 2008
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EXTENSIONS
| More terms from Harvey P. Dale, May 03 2011.
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