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A182041 Number of independent sets of nodes in C_5 X C_n (n >= 1).

%I A182041 #28 Feb 16 2025 08:33:13
%S A182041 11,1,81,391,3561,25531,199821,1511931,11589281,88389661,675443291,
%T A182041 5157630831,39394699881,300868345701,2297915763861,17550293888221,
%U A182041 134040955378561,1023739686467981,7818833928607761,59716490127924211,456085875187977011,3483364700645591901
%N A182041 Number of independent sets of nodes in C_5 X C_n (n >= 1).
%D A182041 M. Golin, Y. C. Leung,  Y. J. Wang and X. R. Yong, Counting structures in grid-graphs, cylinders and tori using transfer matrices: Survey and new results. In: Demetrescu, C., Sedgewick, R., Tamassia, R., (eds.) The Proceedings of the Second Workshop on Analytic Algorithmics and Combinatorics (ANALCO05), SIAM, Philadelphia, (2005),  250-258.
%H A182041 Cesar Bautista, <a href="/A182041/b182041.txt">Table of n, a(n) for n = 0..399</a>
%H A182041 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), #12.7.8.
%H A182041 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A182041 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%H A182041 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (4,27,10,-30,-7,8,-1).
%F A182041 a(n)=4*a(n-1)+27*a(n-2)+10*a(n-3)-30*a(n-4)-7*a(n-5)+8*a(n-6)-a(n-7) with a(0)=11, a(1)=1, a[2]=81, a(3)=391, a(4)=3561, a(5)=25531, a(6)=199821.
%F A182041 G.f.: (-11*x^6+27*x^5+130*x^4-70*x^3-220*x^2-43*x+11)/((x^3-5*x^2-7*x+1)*(x^4-3*x^3-x^2+3*x+1)).
%t A182041 LinearRecurrence[{4,27,10,-30,-7,8,-1},{11,1,81,391,3561,25531,199821},30] (* _Harvey P. Dale_, Mar 06 2013 *)
%K A182041 nonn,easy
%O A182041 0,1
%A A182041 _Cesar Bautista_, Apr 07 2012