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A332750 The number of flips to go from Hamiltonian cycle alpha_n to beta_n in the Cameron graph of size n using Thomason's algorithm.

%I A332750 #27 Mar 18 2020 13:01:47
%S A332750 11,65,265,1005,3749,13927,51683,191735,711243,2638305,9786545,
%T A332750 36302213,134659381,499505271,1852863915,6873009871,25494729643,
%U A332750 94570101217,350798151929,1301249991357,4826854219941,17904723777319,66415748007763,246362448161159,913856392265003
%N A332750 The number of flips to go from Hamiltonian cycle alpha_n to beta_n in the Cameron graph of size n using Thomason's algorithm.
%H A332750 Colin Barker, <a href="/A332750/b332750.txt">Table of n, a(n) for n = 1..1000</a>
%H A332750 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 A332750 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 A332750 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1,0,-1,0,-1).
%F A332750 G.f.: z(1+z)(11+10z+6z^2+4z^3+z^4)/((1-z)(1-3z-2z^2-2z^3-z^4-z^5)).
%F A332750 a(n) = 4*a(n-1) - a(n-2) - a(n-4) - a(n-6) for n>6. - _Colin Barker_, Feb 22 2020
%t A332750 LinearRecurrence[{4, -1, 0, -1, 0, -1}, {11, 65, 265, 1005, 3749, 13927}, 20] (* _Jinyuan Wang_, Feb 22 2020 *)
%o A332750 (PARI) Vec(z*(1+z)*(11+10*z+6*z^2+4*z^3+z^4)/((1-z)*(1-3*z-2*z^2-2*z^3-z^4-z^5)) + O(z^30)) \\ _Jinyuan Wang_, Feb 22 2020
%Y A332750 Cf. A332751 (number of flips from beta_n to gamma_n, same growth rate).
%K A332750 nonn,easy
%O A332750 1,1
%A A332750 _Filip Stappers_, Feb 22 2020
%E A332750 More terms from _Jinyuan Wang_, Feb 22 2020