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 A033517 Number of matchings in graph C_{5} X P_{n}. 2
 1, 11, 342, 9213, 253880, 6974078, 191668283, 5267252351, 144751259054, 3977955684680, 109319496849249, 3004244633718754, 82560623863809043, 2268875354470436757, 62351701497747569760, 1713507386797976483977, 47089453761312228669727, 1294080593187150583795074 (list; graph; refs; listen; history; text; internal format)
 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:=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. = 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

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Last modified December 6 21:43 EST 2023. Contains 367616 sequences. (Running on oeis4.)