A028473 Number of perfect matchings in graph P_{11} X P_{2n}.
1, 144, 51205, 21001799, 8940739824, 3852472573499, 1666961188795475, 722364079570222320, 313196612952258199679, 135818983640055277506397, 58902468764522025160456848, 25545661075321867247577262777, 11079103257893769392837296086025
Offset: 0
Keywords
Links
- Alois P. Heinz, 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.
- Vladeta Jovovic, Explicit formula, generating function and recurrence
- Index entries for linear recurrences with constant coefficients, 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).
Programs
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Mathematica
T[?OddQ, ?OddQ] = 0; 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}]; a[n_] := T[2n, 11] // Round; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 28 2022 *)
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PARI
{a(n) = sqrtint(polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(11, 2, I*x/2)))} \\ Seiichi Manyama, Apr 13 2020
Extensions
Title corrected by Sergey Perepechko, Nov 27 2012