A028486 Number of perfect matchings in graph C_{15} X P_{2n}.

1, 1364, 6323504, 35269184041, 207171729355756, 1240837214254999769, 7491895591984935317759, 45390122553039546330628096, 275408624219475075609746445361, 1672150595320335623747680596071399, 10155382441518040205071335049138555724

Offset: 0

Author

Per H. Lundow

Keywords

• nonn

Comments

For odd values of m the order of recurrence relation for the number of perfect matchings in C_{m} X P_{2n} graph does not exceed 2^floor(m/2). In general, this estimate is accurate, however the case m = 15 is an exception. This sequence obeys the recurrence relation of order 120. - Sergey Perepechko, Apr 28 2015

References

• 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.

Links

• Sergey Perepechko, Table of n, a(n) for n = 0..260
• A. M. Karavaev, S. N. Perepechko, Dimer problem on cylinders: recurrences and generating functions, (in Russian), Matematicheskoe Modelirovanie, 2014, V.26, No.11, pp. 18-22.
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
• Sergey Perepechko, Generating function for A028486

Crossrefs

Cf. A028485, A028484.

Programs

PARI

{a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(15, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020

Formula

a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{15}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1). - Seiichi Manyama, Apr 17 2020

Extensions

a(10) from Alois P. Heinz, Dec 10 2013