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%I #23 Mar 18 2020 13:01:42
%S 6,28,108,400,1486,5516,20464,75912,281590,1044532,3874588,14372392,
%T 53312926,197758868,733566368,2721089680,10093604838,37441198412,
%U 138884309516,515177191104,1910997283694,7088649655580,26294623424272,97537225651992,361804397590486,1342076537863268
%N 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.
%H Colin Barker, <a href="/A332751/b332751.txt">Table of n, a(n) for n = 1..1000</a>
%H K. Cameron, <a href="https://doi.org/10.1016/S0012-365X(00)00260-0">Thomason's algorithm for finding a second hamiltonian circuit through a given edge in a cubic graph is exponential on Krawczyk's graphs</a>, Discrete Mathematics (235), 2001, pp. 69-77.
%H Donald Knuth, <a href="https://www-cs-faculty.stanford.edu/~knuth/fasc8a.ps.gz">The Art of Computer Programming, Pre-fascicle 8a, Hamiltonian paths and cycles</a>, exercise 77, pp. 16, 26-27 (retrieved Feb 22 2020).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1,0,-1,0,-1).
%F 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)).
%F a(n) = 4*a(n-1) - a(n-2) - a(n-4) - a(n-6) for n>6. - _Colin Barker_, Feb 22 2020
%t LinearRecurrence[{4, -1, 0, -1, 0, -1}, {6, 28, 108, 400, 1486, 5516}, 20] (* _Jinyuan Wang_, Feb 22 2020 *)
%o (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
%Y Cf. A332750 (number of flips from alpha_n to beta_n, same growth rate).
%K nonn,easy
%O 1,1
%A _Filip Stappers_, Feb 22 2020
%E More terms from _Jinyuan Wang_, Feb 22 2020