A332751 The number of flips to go from Hamiltonian cycle beta_n to gamma_n in the Cameron graph of size n using Thomason's algorithm.
6, 28, 108, 400, 1486, 5516, 20464, 75912, 281590, 1044532, 3874588, 14372392, 53312926, 197758868, 733566368, 2721089680, 10093604838, 37441198412, 138884309516, 515177191104, 1910997283694, 7088649655580, 26294623424272, 97537225651992, 361804397590486, 1342076537863268
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- K. Cameron, Thomason's algorithm for finding a second hamiltonian circuit through a given edge in a cubic graph is exponential on Krawczyk's graphs, Discrete Mathematics (235), 2001, pp. 69-77.
- Donald Knuth, The Art of Computer Programming, Pre-fascicle 8a, Hamiltonian paths and cycles, exercise 77, pp. 16, 26-27 (retrieved Feb 22 2020).
- Index entries for linear recurrences with constant coefficients, signature (4,-1,0,-1,0,-1).
Crossrefs
Cf. A332750 (number of flips from alpha_n to beta_n, same growth rate).
Programs
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Mathematica
LinearRecurrence[{4, -1, 0, -1, 0, -1}, {6, 28, 108, 400, 1486, 5516}, 20] (* Jinyuan Wang, Feb 22 2020 *) -
PARI
Vec(2*z*(3 + 2*z + z^2 - 2*z^3) / ((1 - z)*(1 - 3*z - 2*z^2 - 2*z^3 - z^4 - z^5)) + O(z^30)) \\ Colin Barker, Feb 22 2020
Formula
G.f.: 2*z*(3+2*z+z^2-2*z^3) / ((1-z)*(1-3*z-2*z^2-2*z^3-z^4-z^5)).
a(n) = 4*a(n-1) - a(n-2) - a(n-4) - a(n-6) for n>6. - Colin Barker, Feb 22 2020
Extensions
More terms from Jinyuan Wang, Feb 22 2020