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Search: id:A140184
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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
1
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| 1, 14, 60, 360, 1904, 10528, 57280, 313472, 1711872, 9355776, 51117056, 279316480, 1526198272, 8339333120, 45566902272, 248982306816
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OFFSET
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1,2
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COMMENT
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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
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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 (ppl(AT)spl.at), Jun 06 2008
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EXAMPLE
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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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CROSSREFS
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Sequence in context: A063492 A051799 A164540 this_sequence A025415 A125849 A003695
Adjacent sequences: A140181 A140182 A140183 this_sequence A140185 A140186 A140187
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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 11 2008
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