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A123304
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Number of edge coverings for the circular ladder C_n x K_2 for n>0 (an edge covering for a graph is a set of edges so that every vertex is adjacent to at least one edge of this set).
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0
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4, 5, 43, 263, 1699, 10895, 69943, 448943, 2881699, 18497135, 118730023, 762108143, 4891844659, 31399932335, 201550911703, 1293721577903, 8304182337859, 53303156937455, 342144045482503, 2196165379031663
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The number of edge coverings for the circle C_n for n>0 is the n-th Lucas number.
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FORMULA
| a(n) = 5*a(n-1)+9*a(n-2)+a(n-3)-2*a(n-4); generating function = (4-15*x-18*x^2-x^3)/((1+x)*(1-6*x-3*x^2+2*x^3)).
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MATHEMATICA
| a[0] = 4; a[1] = 5; a[2] = 43; a[3] = 263; a[n_] := a[n] = 5a[n - 1] + 9a[n - 2] + a[n - 3] - 2a[n - 4]; Table[ a[n], {n, 0, 19}] (* or *) - Robert G. Wilson v Sep 26 2006
CoefficientList[ Series[(4 - 15x - 18x^2 - x^3)/((1 + x)*(1 - 6x - 3x^2 + 2x^3)), {x, 0, 19}], x] - Robert G. Wilson v Sep 26 2006
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CROSSREFS
| Sequence in context: A152291 A041557 A189744 * A041037 A041038 A151486
Adjacent sequences: A123301 A123302 A123303 * A123305 A123306 A123307
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KEYWORD
| nonn
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AUTHOR
| Roberto Tauraso (tauraso(AT)mat.uniroma2.it), Sep 24 2006
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EXTENSIONS
| More terms from Robert G. Wilson v Sep 26 2006
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