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Search: id:A109115
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| A109115 |
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a(n)=4a(n-1)+3a(n-2), a(0)=1, a(1)=6. |
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+0
3
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| 1, 6, 27, 126, 585, 2718, 12627, 58662, 272529, 1266102, 5881995, 27326286, 126951129, 589783374, 2739986883, 12729297654, 59137151265, 274736498022, 1276357445883, 5929639277598, 27547629448041, 127979435624958
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OFFSET
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0,2
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COMMENT
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Kekule numbers for certain benzenoids.
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 302, P_{12}).
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FORMULA
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a(n)=[(sqrt(7)+4)(2+sqrt(7))^n+(sqrt(7)-4)(2-sqrt(7))^n]/[2sqrt(7)]. G.f.=(1+2z)/(1-4z-3z^2).
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MAPLE
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a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=4*a[n-1]+3*a[n-2] od: seq(a[n], n=0..26);
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CROSSREFS
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Sequence in context: A002912 A030297 A045500 this_sequence A038176 A104745 A018901
Adjacent sequences: A109112 A109113 A109114 this_sequence A109116 A109117 A109118
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 19 2005
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