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%I #14 Jun 03 2022 15:17:59
%S 1,1,1,1,2,3,8,30,132,1400,23595,1107260,198172975,156753667213,
%T 1316573850509365,186386043285609148267,1238266675343181339894414632,
%U 1472345944138437490816316070884292123
%N a(n) = (a(n-1) + a(n-3)) * a(n-2) / a(n-4). a(1) = a(2) = a(3) = a(4) = 1.
%H David Gale, <a href="https://doi.org/10.1007/978-1-4612-2192-0_1">Tracking the Automatic Ant</a>, Chapter 1.
%F a(n) * a(n-6) = (a(n-1) + a(n-3)) * (a(n-3) + a(n-5)) for all n in Z. - _Michael Somos_, Dec 25 2013
%F a(5-n) = a(n) for all n in Z. - _Michael Somos_, Dec 25 2013
%F a(n) = 6 * a(n-2) * a(n-3) - (a(n-2) + a(n-3) + a(n-5)) for all n in Z. - _Michael Somos_, May 30 2022
%t a[ n_] := a[n] = If[n < 1, a[5 - n], If[n < 5, 1, (a[n - 1] + a[n - 3]) a[n - 2] / a[n - 4]]]; (* _Michael Somos_, Dec 25 2013 *)
%t a[ n_] := a[n] = If[n < 1, a[5 - n], If[n < 6, Max[1, n - 3], 6*a[n - 2]*a[n-3] - (a[n - 2] + a[n - 3] + a[n - 5])]]; (* _Michael Somos_, May 30 2022 *)
%o (PARI) {a(n) = if( n<1, n = 5-n); if( n<5, 1, (a(n-1) + a(n-3)) * a(n-2) / a(n-4))}; /* _Michael Somos_, Dec 25 2013 */
%o (PARI) {a(n) = if( n<1, n = 5-n); if( n<6, max(1, n-3), 6*a(n-2)*a(n-3) - (a(n-2)+a(n-3)+a(n-5)))}; /* _Michael Somos_, May 30 2022 */
%Y Cf. A078919.
%K nonn
%O 1,5
%A _Benoit Cloitre_, Dec 13 2002
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