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A098648
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Expansion of (1-3*x)/(1-6*x+4*x^2).
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7
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1, 3, 14, 72, 376, 1968, 10304, 53952, 282496, 1479168, 7745024, 40553472, 212340736, 1111830528, 5821620224, 30482399232, 159607914496, 835717890048, 4375875682304, 22912382533632, 119970792472576, 628175224700928
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A001077. Second binomial transform of A084057. Third binomial transform of 1/(1-5*x^2). Let A=[1,1,1,1;3,1,-1,-3;3,-1,-1,3;1,-1,1,-1], the 4 X 4 Krawtchouk matrix. Then a(n)=trace((16(A*A`)^(-1))^n)/4.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
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FORMULA
| E.g.f.: exp(3*x)*cosh(sqrt(5)*x).
a(n) = ((3-sqrt(5))^n+(3+sqrt(5))^n)/2.
a(n) = 2*(3*a(n-1)-2*a(n-2)). - Lekraj Beedassy, Oct 22 2004
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MATHEMATICA
| a[n_]:=(MatrixPower[{{5, 1}, {1, 1}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* From Vladimir Orlovsky, Feb 20 2010 *)
CoefficientList[Series[(1-3x)/(1-6x+4x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -4}, {1, 3}, 31] (* From Harvey P. Dale, June 06 2011 *)
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CROSSREFS
| Cf. A098647.
Sequence in context: A158196 A191649 A009637 * A026295 A118650 A180187
Adjacent sequences: A098645 A098646 A098647 * A098649 A098650 A098651
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 18 2004
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