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A033506 Number of matchings in graph P_{3} X P_{n}. 2
1, 3, 22, 131, 823, 5096, 31687, 196785, 1222550, 7594361, 47177097, 293066688, 1820552297, 11309395995, 70254767718, 436427542283, 2711118571311, 16841658983944, 104621568809247, 649916534985369, 4037327172325542 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, pages 50, 999.

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

LINKS

Table of n, a(n) for n=0..20.

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

R. C. Read, The dimer problem for narrow rectangular arrays: A unified method of solution, and some extensions, Aequationes Mathematicae, 24 (1982), 47-65.

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Index entries for linear recurrences with constant coefficients, signature (4, 14, 0, -10, 0, 1).

FORMULA

G.f.: (1-2*x-x^2)*(1+x-x^2)/((1+x)*(1-5*x-9*x^2+9*x^3+x^4-x^5)). - Sergey Perepechko, Apr 19 2013

MATHEMATICA

CoefficientList[Series[(1 - 2 x - x^2)(1 + x - x^2)/((1 + x)(1 - 5 x - 9 x^2 + 9 x^3 + x^4 - x^5)), {x, 0, 30}], x] (* Harvey P. Dale, Dec 05 2014 *)

LinearRecurrence[{4, 14, 0, -10, 0, 1}, {1, 3, 22, 131, 823, 5096}, 30] (* Harvey P. Dale, Dec 05 2014 *)

Table[RootSum[-1 + # + 9 #^2 - 9 #^3 - 5 #^4 + #^5 &, 1436541 #^n + 3941068 #^(n + 1) - 6086452 #^(n + 2) - 2800519 #^(n + 3) + 591744 #^(n + 4) &]/10204570 - (-1)^n/5, {n, 20}] (* Eric W. Weisstein, Oct 02 2017 *)

CROSSREFS

Column 3 of triangle A210662. Row sums of A100245.

Cf. A030186, A033507, A033508, A033509, A033510, A033511.

Sequence in context: A006283 A232017 A100511 * A091639 A091636 A321003

Adjacent sequences:  A033503 A033504 A033505 * A033507 A033508 A033509

KEYWORD

nonn

AUTHOR

Per H. Lundow

STATUS

approved

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Last modified March 20 20:14 EDT 2019. Contains 321352 sequences. (Running on oeis4.)