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

0,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(Sage)
def A033516_list(prec):
    P.<x> = 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
(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

Crossrefs

Row 4 of A287428.

Sequence in context: A202780 A297804 A218819 * A130629 A137648 A106977

Adjacent sequences: A033513 A033514 A033515 * A033517 A033518 A033519

Keyword

nonn,easy

Author

Per H. Lundow

Status

approved