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A182052 Number of independent sets of nodes in C_6 X C_n (n >= 1). 1


%S 18,1,199,1300,18995,199821,2406862,27285777,317960739,3658040968,

%T 42338077399,488631332773,5646974285234,65218753680549,

%U 753462136109959,8703368091760320,100541026090416195,1161408360176875825,13416320242101088558,154981059170079355117

%N Number of independent sets of nodes in C_6 X C_n (n >= 1).

%D C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), Article 12.7.8

%D 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: C. Demetrescu, R. Sedgewick and R.Tamassia, (eds.) The Proceedings of the Second Workshop on Analytic Algorithmics and Combinatorics (ANALCO05), SIAM, Philadelphia, (2005), 250-258.

%H Cesar Bautista, <a href="/A182052/b182052.txt">Table of n, a(n) for n = 0..399</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (4, 84, 89, -575, -360, 1301, 115, -1032, 295, 119, -36, -4, 1).

%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>

%F a(n) = 4*a(n-1] +84*a(n-2) +89*a(n-3) -575*a(n-4) -360*a(n-5) +1301*a(n-6) +115*a(n-7) -1032*a(n-8) +295*a(n-9) +119*a(n-10) -36*a(n-11) -4*a(n-12) +a(n-13) with a(0)=18, a(1)=1, a(2)=199, a(3)=1300, a(4)=18995, a(5)=199821, a(6)=2406862, a(7)=27285777, a(8)=317960739, a(9)=3658040968, a(10)=42338077399, a(11)=488631332773, a(12)=5646974285234.

%F G.f: (-9*x^12 -67*x^11 +556*x^10 +1162*x^9 -6841*x^8 +1421*x^7 +12335*x^6 -3985*x^5 -7340*x^4 +1182*x^3 +1317*x^2 +71*x-18) / ((x-1) *(x^2-3*x-1) *(x^2-x-1) *(x^3+3*x^2-5*x-1) *(x^5-2*x^4-25*x^3-3*x^2+12*x-1)).

%t LinearRecurrence[{4,84,89,-575,-360,1301,115,-1032,295,119,-36,-4,1},{18,1,199,1300,18995,199821,2406862,27285777,317960739,3658040968,42338077399,488631332773,5646974285234},20](* _Harvey P. Dale_, Nov 24 2012 *)

%K nonn,easy

%O 0,1

%A _Cesar Bautista_, Apr 08 2012

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)