A033517 Number of matchings in graph C_{5} X P_{n}.

1, 11, 342, 9213, 253880, 6974078, 191668283, 5267252351, 144751259054, 3977955684680, 109319496849249, 3004244633718754, 82560623863809043, 2268875354470436757, 62351701497747569760, 1713507386797976483977, 47089453761312228669727, 1294080593187150583795074

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

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 (25,76,-209,-159,119,40,-3,-1).

Formula

G.f.: (1 - 14*x - 9*x^2 + 36*x^3 + 21*x^4 - 2*x^5 - x^6)/(1 - 25*x - 76*x^2 + 209*x^3 + 159*x^4 - 119*x^5 - 40*x^6 + 3*x^7 + x^8). - Alois P. Heinz, Dec 09 2013

Maple

seq(coeff(series((1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1-25*x-76*x^2 +209*x^3+159*x^4-119*x^5-40*x^6+3*x^7+x^8), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 26 2019

Mathematica

LinearRecurrence[{25, 76, -209, -159, 119, 40, -3, -1}, {1, 11, 342, 9213, 253880, 6974078, 191668283, 5267252351}, 30] (* G. C. Greubel, Oct 26 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1 -25*x-76*x^2+209*x^3+159*x^4-119*x^5-40*x^6+3*x^7+x^8)) \\ G. C. Greubel, Oct 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1-25*x-76*x^2+209*x^3+159*x^4-119*x^5 -40*x^6+3*x^7+x^8) )); // G. C. Greubel, Oct 26 2019
(Sage)
def A077952_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1-25*x-76*x^2 +209*x^3 +159*x^4-119*x^5-40*x^6+3*x^7+x^8)).list()
A077952_list(30) # G. C. Greubel, Oct 26 2019
(GAP) a:=[1, 11, 342, 9213, 253880, 6974078, 191668283, 5267252351];; for n in [9..30] do a[n]:=25*a[n-1]+76*a[n-2]-209*a[n-3]-159*a[n-4]+119*a[n-5]+40*a[n-6]=3*a[n-7]-a[n-8]; od; a; # G. C. Greubel, Oct 26 2019

Crossrefs

Row 5 of A287428.

Sequence in context: A091537 A327943 A277348 * A279238 A192841 A158788

Adjacent sequences: A033514 A033515 A033516 * A033518 A033519 A033520

Keyword

nonn,easy

Author

Per H. Lundow

Status

approved