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Somos's sequence {a(5,n)} defined in comment in A018896: a(0)=a(1)= ... = a(11) = 1; for n>=12, a(n) = (a(n-1)*a(n-11) + a(n-6)^2)/a(n-12).
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%I #34 Sep 08 2022 08:46:16

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,11,20,36,61,97,243,425,700,1199,

%T 2183,4115,14902,43515,102827,214168,418685,1223440,3053628,9484929,

%U 31351174,95335734,260010845,1305343146,4437434637,12553187856,35704506092

%N Somos's sequence {a(5,n)} defined in comment in A018896: a(0)=a(1)= ... = a(11) = 1; for n>=12, a(n) = (a(n-1)*a(n-11) + a(n-6)^2)/a(n-12).

%H Seiichi Manyama, <a href="/A271835/b271835.txt">Table of n, a(n) for n = 0..368</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SomosSequence.html">Somos Sequence</a>

%t a[k_,n_]:=a[k,n]= If[n>2k+1,(a[k,(n-1)]*a[k,(n-2k-1)]+(a[k,(n-k-1)])^2 )/a[k,(n-2k-2)],1]; Map[a[5,#]&,Range[0,43]] (* _Peter J. C. Moses_, Apr 15 2016 *)

%t RecurrenceTable[{Table[a[i]==1,{i,0,11}],a[n]==(a[n-1]a[n-11]+a[n-6]^2)/ a[n-12]},a,{n,50}](* _Harvey P. Dale_, Sep 24 2021 *)

%o (PARI) {a(n) = if(n< 12, 1, (a(n-1)*a(n-11) + a(n-6)^2)/a(n-12))};

%o for(n=0,50, print1(a(n), ", ")) \\ _G. C. Greubel_, Feb 21 2018

%o (Magma) [n le 12 select 1 else (Self(n-1)*Self(n-11) + Self(n-6)^2 )/Self(n-12): n in [1..50]]; // _G. C. Greubel_, Feb 21 2018

%Y Cf. A018896, A006125, A006720, A102276, A271341, A271831, A271837, A271838, A271839.

%K nonn

%O 0,13

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Apr 15 2016

%E More terms from _Alois P. Heinz_, Apr 15 2016