A174404 A (4,5)-Somos 4 sequence.

1, 3, 17, 113, 2801, 84771, 4561441, 770238913, 130385366497, 63056004313443, 61225054070593841, 67267054391287018481, 273872013988285333139921, 1422475138861602537117455043, 12376832685202654400796070741057

Offset: 0

Author

Paul Barry, Mar 18 2010

Keywords

• easy
• nonn

Comments

Hankel transform of A174403.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..83
• Paul Barry, Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials, arXiv:1910.00875 [math.CO], 2019.

Programs

Magma

I:=[1,3,17,113]; [n le 4 select I[n] else (4*Self(n-1)*Self(n-3) + 5*Self(n-2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Sep 22 2018

Mathematica

RecurrenceTable[{a[0]==1,a[1]==3,a[2]==17,a[3]==113,a[n]== (4a[n-1] a[n-3]+ 5a[n-2]^2)/a[n-4]},a,{n,20}] (* Harvey P. Dale, May 20 2015 *)

PARI

m=20; v=concat([1,3,17,113], vector(m-4)); for(n=5, m, v[n] = (4*v[n-1]*v[n-3] +5*v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Sep 22 2018

Formula

a(n) = (4*a(n-1)*a(n-3) + 5*a(n-2)^2)/a(n-4), n>=4.