A184019 A (9,-5) Somos-4 sequence.

1, 2, 13, 97, 901, 29186, 1647721, 93837697, 12290566873, 4736355079682, 1969233690270421, 1126004701770879841, 2327721451902521875261, 7371705459667139440634882, 24178816113044965430498802193, 208545961878958994572139555513857, 4688266673793881234527843412398379761

Offset: 0

Author

Paul Barry, Jan 08 2011

Keywords

• nonn

Comments

Hankel transform of A184018.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..75
• Paul Barry, On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences, J. Int. Seq. (2023) Vol. 26, Art. 23.4.7.

Crossrefs

Cf. A184018.

Programs

Magma

I:=[901, 29186, 1647721, 93837697]; [1, 2, 13, 97] cat [n le 4 select I[n] else (9*Self(n-1)*Self(n-3) - 5*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 14 2018

Mathematica

a[n_] := a[n] = (9 a[n - 1] a[n - 3] - 5 a[n - 2]^2)/a[n - 4]; a[0] = 1; a[1] = 2; a[2] = 13; a[3] = 97; Array[a, 17, 0]
RecurrenceTable[{a[0]==1,a[1]==2,a[2]==13,a[3]==97,a[n]==(9a[n-1]a[n-3]- 5a[n-2]^2)/a[n-4]},a[n],{n,20}] (* Harvey P. Dale, Sep 06 2011 *)

Formula

a(n) = (9*a(n-1)*a(n-3) - 5*a(n-2)^2)/a(n-4).