A165904 Somos-4 recurrence with a(i)=2^i for 0<=i<=3.

1, 2, 4, 8, 32, 96, 448, 2944, 15104, 160768, 1565696, 16812032, 341250048, 5081473024, 128940408832, 4153114198016, 110562817540096, 6199850375708672, 294499013825921024, 17095312584100282368, 1743063839902067064832

Offset: 0

Author

Jaume Oliver Lafont, Sep 29 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..148

Crossrefs

Cf. A006720, A157005.

Programs

Magma

I:=[1,2,4,8]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Sep 18 2018

Mathematica

RecurrenceTable[{a[n] == (a[n-1]*a[n-3] +a[n-2]^2)/a[n-4], a[0] == 1, a[1] == 2, a[2] == 4, a[3] == 8}, a, {n, 0, 30}] (* G. C. Greubel, Sep 18 2018 *)

PARI

a(n)=if(n<4,[1,2,4,8][n+1],(a(n-1)*a(n-3)+a(n-2)^2)/a(n-4))

Formula

a(n) = 2^n*A006720(n).

a(n) = (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4). - G. C. Greubel, Sep 18 2018

Extensions

"frac" keyword removed by Jaume Oliver Lafont, Oct 13 2009