A102436 - OEIS

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A102436

Number of matchings of the corona L'(n) of the ladder graph L(n)=P_2 X P_n. and the complete graph K(1); in other words, L'(n) is the graph constructed from L(n) by adding for each vertex v a new vertex v' and the edge vv'.

1, 5, 34, 223, 1469, 9672, 63685, 419329, 2761042, 18179883, 119704137, 788183312, 5189736537, 34171448333, 224999452834, 1481492773799, 9754783005797, 64229669677144, 422915657312253, 2784657839576297, 18335379997029650 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`Row sums of A102435. The number of matchings of the ladder graph L(n)=P_2 X P_n is given in A030186.` `Number of tilings of a 2xn board with squares of 2 colors and dominoes of 1 color [Katz-Stenson]. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 17 2009]`
	LINKS	`M. Katz, C. Stenson, Tiling a 2xn-board with squares and dominoes, J. Int. Seq. 12 (2009) # 09.2.2 [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 17 2009]`
	FORMULA	`a(n)=6a(n-1)+4a(n-2)-a(n-3) for n>=3. G.f.=(1-z)/(1-6z-4z^2+z^3).`
	EXAMPLE	`a(2)=34 because in the graph L'(2) with vertex set {A,B,C,D,a,b,c,d} and edge set {AB,BC,CD,AD,Aa,Bb,Cc,Dd} we have one 0-matching (the empty set), eight` `1-matchings (each edge as a singleton), sixteen 2-matchings (see Example in A102435), eight 3-matchings (any 3-element subset of {Aa,Bb,Cc,Dd} and` `{Aa,Bb,CD},{Bb,Cc,AD},{Cc,Dd,AB},{Aa,Dd,BC}) and one 4-matching ({Aa,Bb,Cc,Dd}).`
	MAPLE	`a[0]:=1: a[1]:=5: a[2]:=34: for n from 3 to 24 do a[n]:=6a[n-1]+4a[n-2]-a[n-3] od: seq(a[n], n=0..24);`
	CROSSREFS	`Cf. A102435, A030186.` `Sequence in context: A127816 A024063 A015545 * A033889 A120469 A180909` `Adjacent sequences: A102433 A102434 A102435 * A102437 A102438 A102439`
	KEYWORD	`nonn`
	AUTHOR	`Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 08 2005`

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Last modified February 15 15:17 EST 2012. Contains 205823 sequences.