A210662 -id:A210662 - cp's OEIS frontend

A288026 Array read by antidiagonals: T(m,n) = number of maximal matchings in the grid graph P_m X P_n.

1, 1, 1, 2, 2, 2, 2, 5, 5, 2, 3, 11, 22, 11, 3, 4, 24, 75, 75, 24, 4, 5, 51, 264, 400, 264, 51, 5, 7, 109, 941, 2357, 2357, 941, 109, 7, 9, 234, 3286, 13407, 22228, 13407, 3286, 234, 9, 12, 503, 11623, 76667, 207423, 207423, 76667, 11623, 503, 12

Offset: 1

Andrew Howroyd, Jun 04 2017

			Table starts:
=====================================================
m\n| 1   2    3     4       5        6          7
---|-------------------------------------------------
1  | 1   1    2     2       3        4          5 ...
2  | 1   2    5    11      24       51        109 ...
3  | 2   5   22    75     264      941       3286 ...
4  | 2  11   75   400    2357    13407      76667 ...
5  | 3  24  264  2357   22228   207423    1922112 ...
6  | 4  51  941 13407  207423  3136370   47256485 ...
7  | 5 109 3286 76667 1922112 47256485 1158560776 ...
...

Andrew Howroyd, Table of n, a(n) for n = 1..276
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

Main diagonal is A287595.
Rows 1-3 are A182097(n+2), A286945, A288028.
Cf. A210662, A099390, A286912, A288025.

A033509 Number of matchings in graph P_{6} X P_{n}.

Original entry on oeis.org

1, 13, 733, 31687, 1453535, 65805403, 2989126727, 135658637925, 6158217253688, 279533139565077, 12688781322524383, 575975678462394151, 26145024935911561519, 1186789728933332428003, 53871436268769248658909

Offset: 0

Per H. Lundow

nonn

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.

F. Cazals, Monomer-Dimer Tilings, 1997.
David Friedhelm Kind, The Gunport Problem: An Evolutionary Approach, De Montfort University (Leicester, UK, 2020).
Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Column 6 of triangle A210662.

Bisection (even part) gives A260035.

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

A033510 Number of matchings in graph P_{7} X P_{n}.

Original entry on oeis.org

1, 21, 2356, 196785, 17525619, 1539222016, 135658637925, 11945257052321, 1052091957273408, 92657526436631289, 8160498611028648795, 718704019165239462736, 63297158846544276862187, 5574656798624151746571203, 490966794038702258639391536, 43240039834820302340627322251

Offset: 0

Per H. Lundow

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..200
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.
Sergey Perepechko, Generating function, May 07 2013
Sergey Perepechko, Text version of generating function

Column 7 of triangle A210662.

Terms a(13) and beyond from Andrew Howroyd, Apr 18 2021

A033512 Number of matchings in graph P_{9} X P_{n}.

Original entry on oeis.org

1, 55, 24342, 7594361, 2548684656, 842518533590, 279533139565077, 92657526436631289, 30721240815429999078, 10185111919160666118608, 3376771882017849561260401, 1119528305492897225312120742, 371166848426649070379972358241, 123056076089539426001744759117065

Offset: 0

Per H. Lundow

nonn

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.

Alois P. Heinz, Table of n, a(n) for n = 0..400
Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Column k=9 of A210662.

A033513 Number of matchings in graph P_{10} X P_{n}.

Original entry on oeis.org

1, 89, 78243, 47177097, 30734932553, 19711134149599, 12688781322524383, 8160498611028648795, 5249581929453966097649, 3376771882017849561260401, 2172138783673094193937750015, 1397239543795157686038029989037, 898783117890438425073750503319527

Offset: 0

Per H. Lundow

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..350
Burton S. Kaliski Jr, Targeted Fibonacci Exponentiation, arXiv preprint arXiv:1711.02491 [math.NT], 2017.
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.

Column k=10 of A210662.

A033514 Number of matchings in graph P_{11} X P_{n}.

Original entry on oeis.org

1, 144, 251498, 293066688, 370635224561, 461148537211748, 575975678462394151, 718704019165239462736, 897032469743945346623442, 1119528305492897225312120742, 1397239543795157686038029989037, 1743829823240164494694386437970640

Offset: 0

Per H. Lundow

nonn

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.

Alois P. Heinz, Table of n, a(n) for n = 0..300
Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Column k=11 of A210662.

cp's OEIS Frontend

A288026 Array read by antidiagonals: T(m,n) = number of maximal matchings in the grid graph P_m X P_n.

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A033509 Number of matchings in graph P_{6} X P_{n}.

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A033510 Number of matchings in graph P_{7} X P_{n}.

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A033512 Number of matchings in graph P_{9} X P_{n}.

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A033513 Number of matchings in graph P_{10} X P_{n}.

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A033514 Number of matchings in graph P_{11} X P_{n}.

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