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Number of perfect matchings in graph P_{11} X P_{2n}.
4

%I #37 Mar 03 2024 10:21:48

%S 1,144,51205,21001799,8940739824,3852472573499,1666961188795475,

%T 722364079570222320,313196612952258199679,135818983640055277506397,

%U 58902468764522025160456848,25545661075321867247577262777,11079103257893769392837296086025

%N Number of perfect matchings in graph P_{11} X P_{2n}.

%H Alois P. Heinz, <a href="/A028473/b028473.txt">Table of n, a(n) for n = 0..200</a>

%H 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 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.

%H Vladeta Jovovic, <a href="/A028473/a028473.pdf">Explicit formula, generating function and recurrence</a>

%H <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (780, -194881, 22377420, -1419219792, 55284715980, -1410775106597, 24574215822780, -300429297446885, 2629946465331120, -16741727755133760, 78475174345180080, -273689714665707178, 716370537293731320, -1417056251105102122, 2129255507292156360, -2437932520099475424, 2129255507292156360, -1417056251105102122, 716370537293731320, -273689714665707178, 78475174345180080, -16741727755133760, 2629946465331120, -300429297446885, 24574215822780, -1410775106597, 55284715980, -1419219792, 22377420, -194881, 780, -1).

%t T[_?OddQ, _?OddQ] = 0;

%t T[m_, n_] := Product[2(2+Cos[2 j Pi/(m+1)]+Cos[2 k Pi/(n+1)]), {k, 1, n/2}, {j, 1, m/2}];

%t a[n_] := T[2n, 11] // Round;

%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 28 2022 *)

%o (PARI) {a(n) = sqrtint(polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(11, 2, I*x/2)))} \\ _Seiichi Manyama_, Apr 13 2020

%Y Row 11 of array A099390.

%Y Bisection of A210724 (even part).

%K nonn

%O 0,2

%A _Per H. Lundow_

%E Title corrected by _Sergey Perepechko_, Nov 27 2012