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A157005 A Somos-4 variant.

%I A157005 #10 Sep 08 2022 08:45:41
%S A157005 1,2,8,24,112,736,3776,40192,391424,4203008,85312512,1270368256,
%T A157005 32235102208,1038278549504,27640704385024,1549962593927168,
%U A157005 73624753456480256,4273828146025070592,435765959975516766208
%N A157005 A Somos-4 variant.
%C A157005 Hankel transform of A157004.
%H A157005 G. C. Greubel, <a href="/A157005/b157005.txt">Table of n, a(n) for n = 0..145</a>
%F A157005 a(n) = (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(0)=1, a(1)=2, a(2)=8, a(3)=24.
%F A157005 a(n) = 2^n*A006720(n+2).
%t A157005 RecurrenceTable[{a[0]==1,a[1]==2,a[2]==8,a[3]==24,a[n]==(a[n-1] a[n-3]+a[n-2]^2)/a[n-4]},a,{n,20}]  (* _Harvey P. Dale_, Apr 30 2011 *)
%o A157005 (PARI) m=20; v=concat([1,2,8,24], vector(m-4)); for(n=5, m, v[n] = (v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Feb 23 2019
%o A157005 (Magma) I:=[1,2,8,24]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..20]]; // _G. C. Greubel_, Feb 23 2019
%o A157005 (Sage)
%o A157005 def a(n):
%o A157005     if (n==0): return 1
%o A157005     elif (n==1): return 2
%o A157005     elif (n==2): return 8
%o A157005     elif (n==3): return 24
%o A157005     else: return (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
%o A157005 [a(n) for n in (0..20)] # _G. C. Greubel_, Feb 23 2019
%o A157005 (GAP) a:=[1,2,8,24];; for n in [5..20] do a[n]:=(a[n-1]*a[n-3] + a[n-2]^2)/a[n-4]; od; a; # _G. C. Greubel_, Feb 23 2019
%Y A157005 Cf. A157101, A162546, A162547.
%K A157005 easy,nonn
%O A157005 0,2
%A A157005 _Paul Barry_, Feb 20 2009