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: Demetrescu, C., Sedgewick, R., Tamassia, R., (eds.) The Proceedings of the Second Workshop on Analytic Algorithmics and Combinatorics (ANALCO05), SIAM, Philadelphia, (2005), 250-258.
LINKS
Cesar Bautista, Table of n, a(n) for n = 0..399
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 (4,27,10,-30,-7,8,-1).
FORMULA
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.
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)).
MATHEMATICA
LinearRecurrence[{4, 27, 10, -30, -7, 8, -1}, {11, 1, 81, 391, 3561, 25531, 199821}, 30] (* Harvey P. Dale, Mar 06 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cesar Bautista, Apr 07 2012
STATUS
approved