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A107979
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a(n)=4a(n-1)+2a(n-2), a(0)=2, a(1)=9.
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1
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2, 9, 40, 178, 792, 3524, 15680, 69768, 310432, 1381264, 6145920, 27346208, 121676672, 541399104, 2408949760, 10718597248, 47692288512, 212206348544, 944209971200, 4201252581888, 18693430269952, 83176226243584
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Kekule numbers for certain benzenoids.
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REFERENCES
| S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 78).
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FORMULA
| O.g.f.: (2+x)/(1-4x-2x^2). a(n)=2*A090017(n)+A090017(n-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2008]
a(n)=1/12*((Sqrt[6]-3)(-(2-Sqrt[6])^n)+(3+Sqrt[6])(2+Sqrt[6])^n) [From Harvey P. Dale, June 21 2011]
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MAPLE
| a[0]:=2: a[1]:=9: for n from 2 to 26 do a[n]:=4*a[n-1]+2*a[n-2] od: seq(a[n], n=0..26);
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MATHEMATICA
| LinearRecurrence[{4, 2}, {2, 9}, 30] (* or *) CoefficientList[Series[(-x-2)/(2x^2+4x-1), {x, 0, 30}], x] (* From Harvey P. Dale, June 21 2011 *)
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CROSSREFS
| Cf. A021001. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2008]
Sequence in context: A097070 A164033 A020728 * A021001 A038112 A052512
Adjacent sequences: A107976 A107977 A107978 * A107980 A107981 A107982
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005
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