cp's OEIS Frontend

A271838 Somos's sequence {a(8,n)} defined in comment in A018896: a(0)=a(1)= ... = a(17) = 1; for n>=18, a(n) = (a(n-1)*a(n-17)+ a(n-9)^2)/a(n-18).

%I A271838 #35 Feb 16 2025 08:33:33
%S A271838 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,14,23,39,64,
%T A271838 100,149,213,294,688,1130,1683,2484,3800,6100,10143,17082,28584,87352,
%U A271838 234714,521145,1013424,1809100,3067659,5075784,8375940,22379904,47848348
%N A271838 Somos's sequence {a(8,n)} defined in comment in A018896: a(0)=a(1)= ... = a(17) = 1; for n>=18, a(n) = (a(n-1)*a(n-17)+ a(n-9)^2)/a(n-18).
%H A271838 Seiichi Manyama, <a href="/A271838/b271838.txt">Table of n, a(n) for n = 0..510</a>
%H A271838 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SomosSequence.html">Somos Sequence</a>
%t A271838 a[k_,n_]:=a[k,n] = If[n>2*k+1,(a[k,(n-1)]*a[k,(n-2*k-1)]+(a[k,(n-k-1)])^2 )/a[k,(n-2*k-2)],1]; Map[a[8,#]&,Range[0,50]] (* _Peter J. C. Moses_, Apr 15 2016 *)
%t A271838 RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]==a[8]==a[9]== a[10]==a[11]==a[12]==a[13]==a[14]==a[15]==a[16]==a[17]==1,a[n]==(a[n-1]a[n-17]+ a[n-9]^2)/a[n-18]},a,{n,60}] (* _Harvey P. Dale_, Jun 30 2023 *)
%o A271838 (PARI) {a(n) = if(n< 18, 1, (a(n-1)*a(n-17) + a(n-9)^2)/a(n-18))};
%o A271838 for(n=0,40, print1(a(n), ", ")) \\ _G. C. Greubel_, Feb 21 2018
%o A271838 (Magma) [n le 18 select 1 else (Self(n-1)*Self(n-17) + Self(n-9)^2 )/Self(n-18): n in [1..40]]; // _G. C. Greubel_, Feb 21 2018
%Y A271838 Cf. A018896, A006125, A006720, A102276, A271341, A271835, A271831, A271837, A271839.
%K A271838 nonn
%O A271838 0,19
%A A271838 _Vladimir Shevelev_ and _Peter J. C. Moses_, Apr 15 2016