A168504 Hankel transform of A168503.

1, 2, 12, 432, 31104, 6718464, 8707129344, 22568879259648, 175495605123022848, 8187922952619753996288, 764031466554854484901625856, 213879912621499745085421535625216

Offset

0,2

Comments

Trivial Somos-4 sequence associated to the elliptic curve y^2 = 1 - 12*x +36*x^2 -24*x^3.

Links

G. C. Greubel, Table of n, a(n) for n = 0..61

Formula

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,....).

a(n) = 36*a(n-1)*a(n-3)/a(n-4).

From Vaclav Kotesovec, Feb 24 2019: (Start)

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).

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)

Mathematica

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 *)
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 *)
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 *)

Prog

(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
(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

Crossrefs

Sequence in context: A012751 A012428 A012786 * A062738 A350790 A296623

Adjacent sequences: A168501 A168502 A168503 * A168505 A168506 A168507

Keyword

easy,nonn

Author

Paul Barry, Nov 27 2009

Status

approved