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%I #10 Sep 08 2022 08:45:46
%S 1,1,-16,-644,-40592,-4821056,17059328,2492895195136,
%T 10659285907800064,86296767700623425536,1081586547380924161458176,
%U -36649408809924048998874742784,-18144416387824430577315746611724288
%N A Somos-4 variant: a(n) = (36*a(n-1)*a(n-3) - 68*a(n-2)^2)/a(n-4).
%C Hankel transform of A162543, A162548.
%H Fung Lam, <a href="/A162546/b162546.txt">Table of n, a(n) for n = 0..67</a>
%t RecurrenceTable[{a[n]==(36*a[n-1]*a[n-3] - 68*a[n-2]^2)/a[n-4], a[0]==1, a[1]==1, a[2]==-16, a[3]==-644}, a, {n,20}] (* _G. C. Greubel_, Feb 23 2019 *)
%o (PARI) m=20; v=concat([1,1,-16,-644], vector(m-4)); for(n=5, m, v[n] = (36*v[n-1]*v[n-3] -68*v[n-2]^2)/v[n-4]); v \\ _G. C. Greubel_, Feb 23 2019
%o (Magma) I:=[1,1,-16,-644]; [n le 4 select I[n] else (36*Self(n-1) *Self(n-3) - 68*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 1
%o elif (n==2): return -16
%o elif (n==3): return -644
%o else: return (36*a(n-1)*a(n-3) - 68*a(n-2)^2)/a(n-4)
%o [a(n) for n in (1..20)] # _G. C. Greubel_, Feb 23 2019
%o (GAP) a:=[1,1,-16,-644];; for n in [5..20] do a[n]:=(36*a[n-1]*a[n-3] - 68*a[n-2]^2)/a[n-4]; od; a; # _G. C. Greubel_, Feb 23 2019
%Y Cf. A157005, A157101, A162547.
%K easy,sign
%O 0,3
%A _Paul Barry_, Jul 05 2009
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