A157005 - OEIS

%I #10 Sep 08 2022 08:45:41

%S 1,2,8,24,112,736,3776,40192,391424,4203008,85312512,1270368256,

%T 32235102208,1038278549504,27640704385024,1549962593927168,

%U 73624753456480256,4273828146025070592,435765959975516766208

%N A Somos-4 variant.

%C Hankel transform of A157004.

%H G. C. Greubel, <a href="/A157005/b157005.txt">Table of n, a(n) for n = 0..145</a>

%F 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 a(n) = 2^n*A006720(n+2).

%t 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 (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 (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 (Sage)

%o def a(n):

%o     if (n==0): return 1

%o     elif (n==1): return 2

%o     elif (n==2): return 8

%o     elif (n==3): return 24

%o     else: return (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)

%o [a(n) for n in (0..20)] # _G. C. Greubel_, Feb 23 2019

%o (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 Cf. A157101, A162546, A162547.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 20 2009