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A028472 Number of perfect matchings in graph P_{10} X P_{n}. 3

%I #30 Mar 03 2024 10:19:05

%S 1,1,89,571,18061,185921,4213133,53175517,1031151241,14479521761,

%T 258584046368,3852472573499,65743732590821,1012747193318519,

%U 16848161392724969,264499788583572499,4337452956682508609,68829675768134027209,1119577238373960926141

%N Number of perfect matchings in graph P_{10} X P_{n}.

%H J. L. Hock and R. B. McQuistan, <a href="https://doi.org/10.1016/0166-218X(84)90083-0">A note on the occupational degeneracy for dimers on a saturated two-dimensional lattice space</a>, Discrete Applied Mathematics, 1984, v.8, 101-104.

%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 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (1, 285, 411, -18027, -20689, 472275, 271027, -6149853, -471319, 42303393, -10402780, -157353820, 58545372, 335484428, -123321948, -429447820, 123321948, 335484428, -58545372, -157353820, 10402780, 42303393, 471319, -6149853, -271027, 472275, 20689, -18027, -411, 285, -1, -1).

%F G.f.: (1 - 197x^2 - 214x^3 + 9741x^4 + 7262x^5 - 202037x^6 - 56736x^7 + 2064705x^8 - 156848x^9 - 11058754x^10 + 2972710x^11 + 32425754x^12 - 10324398x^13 - 54699758x^14 + 15137114x^15 + 54699758x^16 - 10324398x^17 - 32425754x^18 + 2972710x^19 + 11058754x^20 - 156848x^21 - 2064705x^22 - 56736x^23 + 202037x^24 + 7262x^25 - 9741x^26 - 214x^27 + 197x^28 - x^30)/(1 - x - 285x^2 - 411x^3 + 18027x^4 + 20689x^5 - 472275x^6 - 271027x^7 + 6149853x^8 + 471319x^9 - 42303393x^10 + 10402780x^11 + 157353820x^12 - 58545372x^13 - 335484428x^14 + 123321948x^15 + 429447820x^16 - 123321948x^17 - 335484428x^18 + 58545372x^19 + 157353820x^20 - 10402780x^21 - 42303393x^22 - 471319x^23 + 6149853x^24 + 271027x^25 - 472275x^26 - 20689x^27 + 18027x^28 + 411x^29 - 285x^30 + x^31 + x^32). - _Sergey Perepechko_, Nov 27 2012

%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[n, 10] // Round;

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

%o (PARI) {a(n) = sqrtint(polresultant(polchebyshev(10, 2, x/2), polchebyshev(n, 2, I*x/2)))} \\ _Seiichi Manyama_, Apr 13 2020

%Y Row 10 of array A099390.

%K nonn

%O 0,3

%A _Per H. Lundow_

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)