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

Author

Per H. Lundow

Keywords

• nonn
• easy

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).

Crossrefs

Row 5 of A287428.

Programs

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

Magma

R:=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

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 *)

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

Sage

def A077952_list(prec):
    P. = 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

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