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 A033516 Number of matchings in graph C_{4} X P_{n}. 3
 1, 7, 108, 1511, 21497, 305184, 4334009, 61545775, 873996300, 12411393231, 176250978417, 2502894414208, 35542954271729, 504736272807255, 7167628868280044, 101785638086283959, 1445431440583263081, 20526196904667164704, 291487197206091205801 (list; graph; refs; listen; history; text; internal format)
 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:=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. = 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 STATUS approved

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Last modified January 23 22:36 EST 2020. Contains 331177 sequences. (Running on oeis4.)