A387571 Number of matchings in the n-double cone graph.
3, 21, 64, 217, 671, 2052, 6119, 18001, 52288, 150429, 429243, 1216516, 3427659, 9609357, 26821696, 74576737, 206650199, 570877956, 1572754223, 4322192329, 11851475008, 32430381861, 88576465779, 241511251972, 657457204371, 1787147867397, 4851349002304
Offset: 1
Links
- Eric Weisstein's World of Mathematics, Double Cone Graph.
- Eric Weisstein's World of Mathematics, Independent Edge Set.
- Index entries for linear recurrences with constant coefficients, signature (5,-5,-5,5,-1).
Programs
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Mathematica
Table[2 (-1)^(n + 1) + Fibonacci[2 n + 5] + ((5 - 3 Sqrt[5]) (3 - Sqrt[5])^n + (3 + Sqrt[5])^n (5 + 3 Sqrt[5])) n/(5 2^n) , {n, 0, 20}] // Expand seq = LinearRecurrence[{5, -5, -5, 5, -1}, {3, 21, 64, 217, 671, 2052}, 20] CoefficientList[Series[(3 + 6 x - 26 x^2 + 17 x^3 - 4 x^4)/((1 + x) (1 - 3 x + x^2)^2), {x, 0, 20}], x]
Formula
a(n) = 5*a(n-1)-5*a(n-2)-5*a(n-3)+5*a(n-4)-a(n-5).
G.f.: (x*(3+6*x-26*x^2+17*x^3-4*x^4))/((1+x)*(1-3*x+x^2)^2).
Comments