A033515 Number of matchings in graph C_{3} X P_{n}.

1, 4, 32, 228, 1655, 11978, 86731, 627960, 4546684, 32919766, 238352021, 1725762060, 12495193865, 90470101964, 655039004548, 4742739182904, 34339290944491, 248629928211118, 1800178148762579, 13033995507292632, 94371237091674512, 683284752187469642

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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.

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Index entries for linear recurrences with constant coefficients, signature (6,9,0,-1).

Formula

G.f.: (1 - 2*x - x^2)/(1 - 6*x - 9*x^2 + x^4). - Alois P. Heinz, Dec 09 2013

Maple

seq(coeff(series((1-2*x-x^2)/(1-6*x-9*x^2+x^4), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 26 2019

Mathematica

LinearRecurrence[{6, 9, 0, -1}, {1, 4, 32, 228}, 30] (* G. C. Greubel, Oct 26 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1-2*x-x^2)/(1-6*x-9*x^2+x^4)) \\ G. C. Greubel, Oct 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-2*x-x^2)/(1-6*x-9*x^2+x^4) )); // G. C. Greubel, Oct 26 2019
(Sage)
def A033515_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1-2*x-x^2)/(1-6*x-9*x^2+x^4)).list()
A033515_list(30) # G. C. Greubel, Oct 26 2019
(GAP) a:=[1, 4, 32, 228];; for n in [5..30] do a[n]:=6*a[n-1]+9*a[n-2]-a[n-4]; od; a; # G. C. Greubel, Oct 26 2019

Crossrefs

Row 3 of A287428.

Sequence in context: A302742 A300210 A302736 * A300799 A303457 A303451

Adjacent sequences: A033512 A033513 A033514 * A033516 A033517 A033518

Keyword

nonn,easy

Author

Per H. Lundow

Status

approved