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A122884
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The (2,3)-entry in the n-th power of the 3 X 3 matrix M = [1,1,1; 4,2,1; 9,3,1].
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3
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1, 7, 39, 231, 1339, 7819, 45543, 265503, 1547347, 9018835, 52565151, 306373095, 1785671371, 10407659227, 60660275799, 353554011951, 2060663763139, 12010428632419, 70001907900303, 408001019031543, 2378004205764667
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n+1) = 4*a(n) + 11*a(n-1) - 2*a(n-3).
G.f.: x*(1+3*x)/((2*x+1)* (1-6*x+x^2)).
a(n)=-(29/68)*sqrt(2)*[3-2*sqrt(2)]^(n-1)+(19/34)*[3+2*sqrt(2)]^(n-1)+(29/ 68)*[3+2*sqrt(2)]^(n-1) *sqrt(2)+(19/34)*[3-2*sqrt(2)]^(n-1)-(2/17)*(-2)^(n-1), - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 09 2008
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EXAMPLE
| M^2 * [0,0,1] = [3, 7, 13], so the middle term in the last row is 7 = a(2).
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CROSSREFS
| Cf. A122883, A122885, A122886.
Sequence in context: A125786 A155589 A071082 * A139173 A138417 A207154
Adjacent sequences: A122881 A122882 A122883 * A122885 A122886 A122887
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), Sep 17 2006
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EXTENSIONS
| More terms from Paolo P. Lava (paoloplava(AT)gmail.com), Jul 09 2008
Definition replaced by a precise phrase by the Assoc. Editors of the OEIS, Mar 12 2010.
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