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%I #29 Sep 13 2023 12:24:20
%S 7,1,35,121,743,3561,18995,96433,500871,2573905,13292995,68492073,
%T 353290343,1821383097,9392360019,48428332641,249716406791,
%U 1287608913057,6639354593123,34234612471001,176524935990503,910219628918665,4693389213891699,24200638961917201
%N Number of independent sets of nodes in C_4 X C_n (n > 2).
%H Colin Barker, <a href="/A050402/b050402.txt">Table of n, a(n) for n = 0..1000</a>
%H C. Bautista-Ramos and C. Guillen-Galvan, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Bautista/bautista4.html">Fibonacci numbers of generalized Zykov sums</a>, J. Integer Seq., 15 (2012), Article 12.7.8
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,15,8,-7,-2,1).
%F 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).
%F 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
%p 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
%t 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]
%o (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
%o (Magma) R<x>:=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
%o (Sage)
%o def A050402_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o 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()
%o A050402_list(30) # _G. C. Greubel_, Oct 30 2019
%o (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
%K easy,nonn
%O 0,1
%A _Stephen G Penrice_, Dec 21 1999
%E More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
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