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A033509 Number of matchings in graph P_{6} X P_{n}. 3
1, 13, 733, 31687, 1453535, 65805403, 2989126727, 135658637925, 6158217253688, 279533139565077, 12688781322524383, 575975678462394151, 26145024935911561519, 1186789728933332428003, 53871436268769248658909 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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..14.

F. Cazals, Monomer-Dimer Tilings, 1997.

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

FORMULA

G.f.: (1 -23*x -311*x^2 +3891*x^3 +12057*x^4 -218447*x^5 +315889*x^6 +2997721*x^7 -8754480*x^8 -13467571*x^9 +66016499*x^10 +14684235*x^11 -240612231*x^12 +56233657*x^13 +496137395*x^14 -207743591*x^15 -612805499*x^16 +303976032*x^17 +458919487*x^18 -249194245*x^19 -206819317*x^20 +123372421*x^21 +54160427*x^22 -37223601*x^23 -7443809*x^24 +6708699*x^25 +338040*x^26 -686517*x^27 +29377*x^28 +36273*x^29 -3521*x^30 -861*x^31 +109*x^32 +7*x^33 -x^34) / (1 -36*x -576*x^2 +6080*x^3 +42422*x^4 -453004*x^5 -443404*x^6 +12931566*x^7 -25517604*x^8 -83558644*x^9 +295510396*x^10 +154307596*x^11 -1335612340*x^12 +274712602*x^13 +3235975264*x^14 -1630080704*x^15 -4669345206*x^16 +2978277152*x^17 +4169343006*x^18 -2919950172*x^19 -2310327672*x^20 +1717916424*x^21 +777289050*x^22 -626694028*x^23 -149620588*x^24 +141424642*x^25 +13835164*x^26 -19237868*x^27 -94620*x^28 +1503868*x^29 -81796*x^30 -62874*x^31 +5736*x^32 +1224*x^33 -138*x^34 -8*x^35 +x^36). - Sergey Perepechko, May 04 2013

CROSSREFS

Column 6 of triangle A210662.

Bisection (even part) gives A260035.

Sequence in context: A108223 A114355 A086157 * A262099 A060825 A182932

Adjacent sequences:  A033506 A033507 A033508 * A033510 A033511 A033512

KEYWORD

nonn

AUTHOR

Per H. Lundow

STATUS

approved

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Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.