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A182052 Number of independent sets of nodes in C_6 X C_n (n >= 1). 1
18, 1, 199, 1300, 18995, 199821, 2406862, 27285777, 317960739, 3658040968, 42338077399, 488631332773, 5646974285234, 65218753680549, 753462136109959, 8703368091760320, 100541026090416195, 1161408360176875825, 13416320242101088558, 154981059170079355117 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
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.
LINKS
C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), #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 (4,84,89,-575,-360,1301,115,-1032,295,119,-36,-4,1).
FORMULA
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.
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)).
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A040341 A111872 A089275 * A223520 A242567 A040319
KEYWORD
nonn,easy
AUTHOR
Cesar Bautista, Apr 08 2012
STATUS
approved

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Last modified June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)