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A033507 Number of matchings in graph P_{4} X P_{n}. 6
1, 5, 71, 823, 10012, 120465, 1453535, 17525619, 211351945, 2548684656, 30734932553, 370635224561, 4469527322891, 53898461609719, 649966808093412, 7838012982224913, 94519361817920403, 1139818186429110279, 13745178487929574337, 165754445655292452448 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

H. Hosoya and A. Motoyama, An effective algorithm for obtaining polynomials for dimer statistics. Application of operator technique on the topological index to two- and three-dimensional rectangular and torus lattices, J. Math. Phys., 26(1985), 157-167.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

Per Hakan Lundow, Computation of matching polynomials and the number of 1-factors in polygraphs, Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Index entries for linear recurrences with constant coefficients, signature (9, 41, -41, -111, 91, 29, -23, -1, 1).

FORMULA

From Sergey Perepechko, Apr 24 2013: (Start)

a(n) = 9*a(n-1)+41*a(n-2)-41*a(n-3)-111*a(n-4)+91*a(n-5)+29*a(n-6)-23*a(n-7) -a(n-8) +a(n-9).

G.f.: (1-x) * (1 -3*x -18*x^2 +2*x^3 +12*x^4 +x^5 -x^6) / (1 -9*x -41*x^2 +41*x^3 +111*x^4 -91*x^5 -29*x^6 +23*x^7 +x^8 -x^9). (End)

EXAMPLE

a(1) = 5: the graph is

. o-o-o-o

and the five matchings are

. o o o o

. o-o o o

. o o-o o

. o o o-o

. o-o o-o

MAPLE

a:=array(0..20, [1, 5, 71, 823, 10012, 120465, 1453535, 17525619, 211351945]):

for j from 9 to 20 do

  a[j]:=9*a[j-1]+41*a[j-2]-41*a[j-3]-111*a[j-4]+91*a[j-5]+

        29*a[j-6]-23*a[j-7]-a[j-8]+a[j-9]

od:

convert(a, list);

# Sergey Perepechko, Apr 24 2013

MATHEMATICA

LinearRecurrence[{9, 41, -41, -111, 91, 29, -23, -1, 1}, {1, 5, 71, 823, 10012, 120465, 1453535, 17525619, 211351945}, 30] (* Harvey P. Dale, Mar 27 2015 *)

CROSSREFS

Column 4 of triangle A210662. Row sums of A100265.

For perfect matchings see A005178.

Cf. A033508-A033511.

Bisection (even part) gives A260034.

Sequence in context: A197427 A197668 A064752 * A092250 A193436 A193501

Adjacent sequences:  A033504 A033505 A033506 * A033508 A033509 A033510

KEYWORD

nonn

AUTHOR

Per H. Lundow

EXTENSIONS

Edited by N. J. A. Sloane, Nov 15 2009

STATUS

approved

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Last modified March 26 16:31 EDT 2017. Contains 284137 sequences.