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A140766
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a(n) = 6*a(n-1) - 6*a(n-2).
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1
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1, 5, 24, 114, 540, 2556, 12096, 57240, 270864, 1281744, 6065280, 28701216, 135815616, 642686400, 3041224704, 14391229824, 68100030720, 322252805376, 1524916647936, 7215983055360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Companion sequence = A030192 beginning (1, 6, 30, 144, 684,...).
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FORMULA
| a(n) = 6*a(n-1) - 6*a(n-2); given a(1) = 1, a(2) = 5. Term (1,1) of X^n, where X = the 3x3 matrix [1,1,1; 1,2,1; 3,1,3].
O.g.f.: x(1-x)/(1-6x+6x^2). a(n)=A030192(n-1)-A030192(n-2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2008
a(n)=(1/2)*[3-sqrt(3)]^n+(1/3)*sqrt(3)*[3+sqrt(3)]^n+(1/2)*[3+sqrt(3)]^n-(1/3)*[3-sqrt(3)]^n *sqrt(3), with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2008
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EXAMPLE
| a(5) = 540 = 6*a(4) - 6*a(3) = 6*(114) - 6*24.
a(5) = 540 = term (1,1) of X^5.
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CROSSREFS
| Cf. A030192.
Sequence in context: A081104 A079028 A141223 * A026388 A057969 A004254
Adjacent sequences: A140763 A140764 A140765 * A140767 A140768 A140769
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), May 28 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2008
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