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%I #10 Sep 08 2022 08:45:49
%S 1,2,12,432,31104,6718464,8707129344,22568879259648,
%T 175495605123022848,8187922952619753996288,
%U 764031466554854484901625856,213879912621499745085421535625216
%N Hankel transform of A168503.
%C Trivial Somos-4 sequence associated to the elliptic curve y^2 = 1 - 12*x +36*x^2 -24*x^3.
%H G. C. Greubel, <a href="/A168504/b168504.txt">Table of n, a(n) for n = 0..61</a>
%F a(n) = Product{k=0..n} a(k)^(n-k), where a(n) is the sequence (2, 3, 6, 2, 3, 6, 2, 3, 6,....).
%F a(n) = 36*a(n-1)*a(n-3)/a(n-4).
%F From _Vaclav Kotesovec_, Feb 24 2019: (Start)
%F a(n) = 2^((3*n*(n+1) + 1 - 2*cos((2*n+1)*Pi/3))/9)*3^((3*n^2 - 2 + 2*cos(2*n*Pi/3))/9).
%F a(n) = 2^((n*(n+2) - floor(n/3) - 2*floor((n+1)/3))/3) * 3^((n*(n-1) + 2*floor(n/3) + floor((n+1)/3))/3). (End)
%t RecurrenceTable[{a[n] == 36*a[n-1]*a[n-3]/a[n-4], a[0] == 1, a[1] == 2, a[2] == 12, a[3] == 432}, a, {n, 0, 20}] (* _G. C. Greubel_, Sep 18 2018 *)
%t Table[2^((3*n*(n+1) + 1 - 2*Cos[(2*n+1)*Pi/3])/9)*3^((3*n^2 - 2 + 2*Cos[2*n*Pi/3])/9), {n, 0, 15}] (* _Vaclav Kotesovec_, Feb 24 2019 *)
%t Table[2^((n*(n + 2) - Floor[n/3] - 2*Floor[(n + 1)/3])/3) * 3^((n*(n - 1) + 2*Floor[n/3] + Floor[(n + 1)/3])/3), {n, 0, 15}] (* _Vaclav Kotesovec_, Feb 24 2019 *)
%o (PARI) m=20; v=concat([1,2,12,432], vector(m-4)); for(n=5, m, v[n] = 36*v[n-1]*v[n-3]/v[n-4]); v \\ _G. C. Greubel_, Sep 18 2018
%o (Magma) I:=[1,2,12,432]; [n le 4 select I[n] else 36*Self(n-1)*Self(n-3)/Self(n-4): n in [1..20]]; // _G. C. Greubel_, Sep 18 2018
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 27 2009
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