cp's OEIS Frontend

A033508 Number of matchings in graph P_{5} X P_{n}.

%I A033508 #20 May 06 2016 13:01:46
%S A033508 1,8,228,5096,120465,2810694,65805403,1539222016,36012826776,
%T A033508 842518533590,19711134149599,461148537211748,10788744980331535,
%U A033508 252406631116215534,5905146419664967132,138153075553825008696
%N A033508 Number of matchings in graph P_{5} X P_{n}.
%C A033508 These are the row sums of the following triangle of the matchings of P_5 X P_n with k>=0 monomers (A003775 appears in the first column):
%C A033508 1;
%C A033508 0, 3, 0, 4, 0, 1;
%C A033508 8, 0, 56, 0, 94, 0, 56, 0, 13, 0, 1;
%C A033508 0, 106, 0, 757, 0, 1670, 0, 1597, 0, 758, 0, 185, 0, 22, 0, 1;
%C A033508 95, 0, 2111, 0, 12181, 0, 29580, 0, 36771, 0, 25835, 0, 10769, 0, 2696, 0, 395, 0, 31, 0, 1;
%C A033508 0, 2180, 0, 35104, 0, 192672, 0, 510752, 0, 762180, 0, 695848, 0, 407620, 0, 157000, 0, 39979, 0, 6632, 0, 686, 0, 40, 0, 1;
%C A033508 1183, 0, 52614, 0, 611633, 0, 3146447, 0, 8803727, 0, 14957414, 0, 16492039, 0, 12307901, 0, 6380454, 0, 2329148, 0, 600254, 0, 108186, 0, 13295, 0, 1058, 0, 49, 0, 1;
%C A033508 0, 37924, 0, 1054776, 0, 10405842, 0, 51732687, 0, 151233778, 0, 283790459, 0, 361377070, 0, 324069497, 0, 209807278, 0, 99625091, 0, 34985010, 0, 9096697, 0, 1740018, 0, 240905, 0, 23414, 0, 1511, 0, 58, 0, 1;
%C A033508 - _R. J. Mathar_, May 06 2016
%H A033508 F. Cazals, <a href="http://algo.inria.fr/libraries/autocomb/MonoDiMer-html/MonoDiMer.html">Monomer-Dimer Tilings</a>, 1997.
%H A033508 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors.pdf">Computation of matching polynomials and the number of 1-factors in polygraphs</a>, Research report, No 12, 1996, Department of Math., Umea University, Sweden.
%H A033508 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.
%F A033508 For g.f. see Maple program. - _Sergey Perepechko_, Apr 26 2013
%p A033508 # The following g.f. is for the sequence a(0)=1, a(1)=8, a(2)=228, etc.
%p A033508 Gf:= (1-6*x-113*x^2+88*x^3+1794*x^4-1994*x^5-6956*x^6+7532*x^7+
%p A033508 11175*x^8-9448*x^9-9255*x^10+4700*x^11+3820*x^12-870*x^13-654*x^14+
%p A033508 68*x^15+45*x^16-2*x^17-x^18)/(1-14*x-229*x^2+16*x^3+4757*x^4-898*x^5-
%p A033508 35106*x^6+26564*x^7+74665*x^8-60482*x^9-73623*x^10+50158*x^11+
%p A033508 38553*x^12-17604*x^13-10366*x^14+2538*x^15+1281*x^16-140*x^17-65*x^18+
%p A033508 2*x^19+x^20):
%p A033508 expr:=convert(series(Gf,x,21),polynom):
%p A033508 seq(coeff(expr,x,j),j=0..20);
%p A033508 # _Sergey Perepechko_, Apr 26 2013
%Y A033508 Column 5 of triangle A210662.
%K A033508 nonn
%O A033508 0,2
%A A033508 _Per H. Lundow_