This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182052 #32 Feb 16 2025 08:33:13
%S A182052 18,1,199,1300,18995,199821,2406862,27285777,317960739,3658040968,
%T A182052 42338077399,488631332773,5646974285234,65218753680549,
%U A182052 753462136109959,8703368091760320,100541026090416195,1161408360176875825,13416320242101088558,154981059170079355117
%N A182052 Number of independent sets of nodes in C_6 X C_n (n >= 1).
%D A182052 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 A182052 Cesar Bautista, <a href="/A182052/b182052.txt">Table of n, a(n) for n = 0..399</a>
%H A182052 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 A182052 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A182052 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%H A182052 <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).
%F A182052 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 A182052 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 A182052 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 A182052 nonn,easy
%O A182052 0,1
%A A182052 _Cesar Bautista_, Apr 08 2012