login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A028468 Number of perfect matchings in graph P_{6} X P_{n}. 7
1, 1, 13, 41, 281, 1183, 6728, 31529, 167089, 817991, 4213133, 21001799, 106912793, 536948224, 2720246633, 13704300553, 69289288909, 349519610713, 1765722581057, 8911652846951, 45005025662792 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

R. P. Stanley, Enumerative Combinatorics I, p. 292.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamilton cycles in product graphs

F. Faase, Results from the counting program

David Klarner, Jordan Pollack, Domino tilings of rectangles with fixed width, Disc. Math. 32 (1980) 45-52

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.

R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 5.

Index entries for linear recurrences with constant coefficients, signature (1,20,10,-38,-10,20,-1,-1).

FORMULA

a(1) = 1,

a(2) = 13,

a(3) = 41,

a(4) = 281,

a(5) = 1183,

a(6) = 6728,

a(7) = 31529,

a(8) = 167089,

a(9) = 817991,

a(10) = 4213133,

a(11) = 21001799,

a(12) = 106912793,

a(13) = 536948224,

a(14) = 2720246633, and

a(n) = 40a(n-2) - 416a(n-4) + 1224a(n-6) - 1224a(n-8) + 416a(n-10) - 40a(n-12) + a(n-14).

G.f.: -(x^2-2*x-1)*(x^4+2*x^3-3*x^2-2*x+1) / ( (x-1) *(1+x) *(x^3-5*x^2+6*x-1) *(x^3+6*x^2+5*x+1) ).

PROG

(PARI) x='x+O('x^200); Vec(-(x^2-2*x-1)*(x^4+2*x^3-3*x^2-2*x+1)/((x-1)*(1+x)*(x^3-5*x^2+6*x-1)*(x^3+6*x^2+5*x+1))) \\ Altug Alkan, Mar 23 2016

CROSSREFS

Row 6 of arrays A099390, A189006.

Column k=2 of A251072.

Cf. A005178.

Sequence in context: A231885 A167240 A147247 * A146995 A102130 A080186

Adjacent sequences:  A028465 A028466 A028467 * A028469 A028470 A028471

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Per H. Lundow

EXTENSIONS

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 26 18:45 EDT 2017. Contains 284137 sequences.