A033516 Number of matchings in graph C_{4} X P_{n}.

1, 7, 108, 1511, 21497, 305184, 4334009, 61545775, 873996300, 12411393231, 176250978417, 2502894414208, 35542954271729, 504736272807255, 7167628868280044, 101785638086283959, 1445431440583263081, 20526196904667164704, 291487197206091205801

Offset: 0

Author

Per H. Lundow

Keywords

• nonn
• easy

References

• Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..800
• J. L. Hock, R. B. McQuistan< The occupation statistics for indistinguishable dumbbells on a 2X2XN lattice space, J. Math. Phys 24 (7) (1983) 1859, Table 1.
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
• Index entries for linear recurrences with constant coefficients, signature (14,6,-46,18,2,-1).

Crossrefs

Row 4 of A287428.

Programs

GAP

a:=[1,7,108,1511,21497,305184];; for n in [4..30] do a[n]:=14*a[n-1]+6*a[n-2]-46*a[n-3]+18*a[n-4]+2*a[n-5]-a[n-6]; od; a; # G. C. Greubel, Oct 26 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2+46*x^3-18*x^4-2*x^5+x^6) )); // G. C. Greubel, Oct 26 2019

Maple

seq(coeff(series((1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2+46*x^3-18*x^4 -2*x^5+x^6), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 26 2019

Mathematica

LinearRecurrence[{14,6,-46,18,2,-1}, {1,7,108,1511,21497,305184}, 30] (* G. C. Greubel, Oct 26 2019 *)

PARI

my(x='x+O('x^30)); Vec((1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2 +46*x^3-18*x^4-2*x^5+x^6)) \\ G. C. Greubel, Oct 26 2019

Sage

def A033516_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2+46*x^3-18*x^4-2*x^5 +x^6) ).list()
A033516_list(30) # G. C. Greubel, Oct 26 2019

Formula

G.f.: -(x^4 -3*x^3 -4*x^2 +7*x -1) / (x^6 -2*x^5 -18*x^4 +46*x^3 -6*x^2 -14*x +1). - Alois P. Heinz, Dec 09 2013