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A271341 Somos's sequence {a(4,n)} defined in comment in A018896.

%I A271341 #22 Sep 08 2022 08:46:16
%S A271341 1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,10,19,35,60,156,284,499,930,1836,7116,
%T A271341 21586,52869,115344,356076,972840,3350009,11844969,37689894,215136930,
%U A271341 785604755,2444023816,7985904285,36968693334,230985863335,1429813280831,6838592493455,27144055289355,191201731942399
%N A271341 Somos's sequence {a(4,n)} defined in comment in A018896.
%C A271341 The sequence of the first differences begins from 9 zeros, 5 1's and 4 consecutive squares, beginning with 2^2.
%C A271341 A generalization see in the comment in A018896.
%H A271341 Seiichi Manyama, <a href="/A271341/b271341.txt">Table of n, a(n) for n = 0..318</a>
%t A271341 k = 4; Set[#, 1] & /@ Map[a[k, #] &, Range[0, 2 k + 1]]; a[k_, n_] /;
%t A271341 n >= 2 k + 2 := (a[k, n - 1] a[k, n - 2 k - 1] + a[k, n - k - 1]^2) / a[k, n - 2 k - 2]; Table[a[k, n], {n, 0, 42}] (* _Michael De Vlieger_, Apr 04 2016 *)
%t A271341 a[n_ /; 0 <= n <= 10] = 1; a[n_]:= a[n] = (a[n-1]*a[n-9] + a[n-5]^2)/a[n -10]; Table[a[n], {n,0,40}] (* _G. C. Greubel_, Feb 21 2018 *)
%o A271341 (PARI) {a(n) = if(n< 10, 1, (a(n-1)*a(n-9) + a(n-5)^2)/a(n-10))};
%o A271341 for(n=0,40, print1(a(n), ", ")) \\ _G. C. Greubel_, Feb 21 2018
%o A271341 (Magma) [n le 10 select 1 else (Self(n-1)*Self(n-9) + Self(n-5)^2 )/Self(n-10): n in [1..40]]; // _G. C. Greubel_, Feb 21 2018
%Y A271341 Cf. A018896, A006720, A102276, A271835, A271831, A271837, A271838, A271839.
%K A271341 nonn
%O A271341 0,11
%A A271341 _Vladimir Shevelev_ and _Peter J. C. Moses_, Apr 04 2016
%E A271341 More terms from _Michael De Vlieger_, Apr 04 2016