Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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