%I #20 Jun 05 2024 19:33:58
%S 1,1,1,1,1,1,1,1,1,2,5,14,41,121,353,989,2393,9397,49121,342793,
%T 2842633,24619238,211654405,1731275594,11581792513,107195509553,
%U 1126517154817,16124559341513,342648008481505,8465982933121657,213444061953471233
%N A Somos 9-type recurrence: a(n) = (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9), with a(0)=...=a(8)=1.
%H G. C. Greubel, <a href="/A122055/b122055.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9).
%p a:= proc (n) option remember;
%p if n < 9 then 1
%p else (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9)
%p fi;
%p end proc;
%p seq(a(n), n=0..35); # _G. C. Greubel_, Oct 03 2019
%t a[n_]:= a[n]= If[n<9, 1, (3*a[n-1]*a[n-8] -a[n-4]*a[n-5])/a[n-9]];
%t Table[a[n], {n, 0, 30}] (* modified by _G. C. Greubel_, Oct 03 2019 *)
%t nxt[{a_,b_,c_,d_,e_,f_,g_,h_,i_}]:={b,c,d,e,f,g,h,i,(3i*b-f*e)/a}; NestList[nxt,PadRight[{},9,1],30][[;;,1]] (* _Harvey P. Dale_, Jun 05 2024 *)
%o (PARI) m=35; v=concat([1,1,1,1,1,1,1,1,1], vector(m-9)); for(n=10, m, v[n] = (3*v[n-1]*v[n-8] - v[n-4]*v[n-5])/v[n-9] ); v \\ _G. C. Greubel_, Oct 03 2019
%o (Magma) [n le 10 select 1 else (3*Self(n-1)*Self(n-8) - Self(n-4)*Self(n-5))/Self(n-9): n in [1..35]]; // _G. C. Greubel_, Oct 03 2019
%o (Sage)
%o def a(n):
%o if n<10: return 1
%o else: return (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9)
%o [a(n) for n in (0..35)] # _G. C. Greubel_, Oct 03 2019
%o (GAP)
%o a:= function(n)
%o if n<10 then return 1;
%o else return (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9);
%o fi;
%o end;
%o List([0..35], n-> a(n) ); # _G. C. Greubel_, Oct 03 2019
%Y Cf. A122025.
%K nonn
%O 0,10
%A _Roger L. Bagula_, Sep 13 2006
%E Name edited and offset changed by _G. C. Greubel_, Oct 03 2019