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 A050402 Number of independent sets of nodes in C_4 X C_n (n > 2). 1
 7, 1, 35, 121, 743, 3561, 18995, 96433, 500871, 2573905, 13292995, 68492073, 353290343, 1821383097, 9392360019, 48428332641, 249716406791, 1287608913057, 6639354593123, 34234612471001, 176524935990503, 910219628918665, 4693389213891699, 24200638961917201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), Article 12.7.8 Eric Weisstein's World of Mathematics, Independent Vertex Set Eric Weisstein's World of Mathematics, Torus Grid Graph Index entries for linear recurrences with constant coefficients, signature (2,15,8,-7,-2,1). FORMULA a(n) = a(n-1) + 17*a(n-2) + 23*a(n-3) + a(n-4) - 9*a(n-5) - a(n-6) + a(n-7). G.f.: (7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3)). - Colin Barker, Aug 31 2012 MAPLE seq(coeff(series((7-13*x-72*x^2-20*x^3+17*x^4+x^5)/((1+x)*(1+2*x-x^2) *(1-5*x-x^2+x^3)), x, n+1), x, n), n = 0 ..30); # G. C. Greubel, Oct 30 2019 MATHEMATICA CoefficientList[Series[(7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3)), {x, 0, 30}], x] PROG (PARI) Vec((7-13*x-72*x^2-20*x^3+17*x^4+x^5)/((1+x)*(1+2*x-x^2)*(1-5*x- x^2+x^3)) + O(x^30)) \\ Colin Barker, May 11 2017 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3)) )); // G. C. Greubel, Oct 30 2019 (Sage) def A050402_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((7 -13*x -72*x^2 -20*x^3 +17*x^4 +x^5)/((1+x)*(1+2*x-x^2)*(1-5*x-x^2+x^3))).list() A050402_list(30) # G. C. Greubel, Oct 30 2019 (GAP) a:=[7, 1, 35, 121, 743, 3561];; for n in [7..30] do a[n]:=2*a[n-1] +15*a[n-2]+8*a[n-3]-7*a[n-4]-2*a[n-5]-a[n-6]; od; a; # G. C. Greubel, Oct 30 2019 CROSSREFS Sequence in context: A002678 A147482 A171770 * A027643 A373036 A225122 Adjacent sequences: A050399 A050400 A050401 * A050403 A050404 A050405 KEYWORD easy,nonn AUTHOR Stephen G Penrice, Dec 21 1999 EXTENSIONS More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999 STATUS approved

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Last modified June 17 11:15 EDT 2024. Contains 373445 sequences. (Running on oeis4.)