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
(SageMath)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved