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A028471 Number of perfect matchings (or domino tilings) in the graph P_9 X P_2n. 3
1, 55, 6336, 817991, 108435745, 14479521761, 1937528668711, 259423766712000, 34741645659770711, 4652799879944138561, 623139489426439754945, 83456125990631342400791, 11177167872295392172767936, 1496943834332592837945956455, 200483802581126644843760725601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

J. L. Hock and R. B. McQuistan, A note on the occupational degeneracy for dimers on a saturated two-dimensional lattice space, Discrete Applied Mathematics, 1984, v.8, 101-104.

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.

LINKS

Table of n, a(n) for n=0..14.

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

FORMULA

a[n] = 209a[n - 1] - 11936a[n - 2] + 274208a[n - 3] - 3112032a[n - 4] + 19456019a[n - 5] - 70651107a[n - 6] + 152325888a[n - 7] - 196664896a[n - 8] + 152325888a[n - 9] - 70651107a[n - 10] + 19456019a[n - 11] - 3112032a[n - 12] + 274208a[n - 13] - 11936a[n - 14] + 209a[n - 15] - a[n - 16]. - Jay Anderson (horndude77(AT)gmail.com), Apr 07 2007

G.f.: (1 - 154x + 6777x^2 - 123961x^3 + 1132714x^4 - 5684515x^5 + 16401668x^6 - 27757938x^7 + 27757938*x^8 - 16401668x^9 + 5684515x^10 - 1132714x^11 + 123961x^12 -6777x^13 + 154x^14 - x^15)/(1 - 209x + 11936x^2 - 274208x^3 + 3112032x^4 - 19456019x^5 + 70651107x^6 - 152325888x^7 + 196664896x^8 - 152325888x^9 + 70651107x^10 -19456019x^11 + 3112032x^12 - 274208x^13 + 11936x^14 - 209x^15 + x^16). - Sergey Perepechko, Nov 23 2012

CROSSREFS

Cf. A000045, A001835, A005178, A003775, A028468, A028469, A028470.

Row 9 of array A099390.

Sequence in context: A060204 A231783 A114049 * A004708 A269500 A090813

Adjacent sequences:  A028468 A028469 A028470 * A028472 A028473 A028474

KEYWORD

nonn

AUTHOR

Per H. Lundow

EXTENSIONS

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified February 21 00:47 EST 2018. Contains 299388 sequences. (Running on oeis4.)