A165905 Somos-4 recurrence with a(0)=1, a(1)=2, a(2)=4, a(3)=16.
1, 2, 4, 16, 48, 224, 1472, 7552, 80384, 782848, 8406016, 170625024, 2540736512, 64470204416, 2076557099008, 55281408770048, 3099925187854336, 147249506912960512, 8547656292050141184, 871531919951033532416
Offset: 0
Keywords
Examples
G.f. = 1 + 2*x + 4*x^2 + 16*x^3 + 224*x^4 + 1472*x^5 + 7552*x^6 + ... - _Michael Somos_, Sep 19 2018
Links
- G. C. Greubel, Table of n, a(n) for n = 0..147
Programs
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Magma
I:=[1,2,4,16]; [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
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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] == 16}, a, {n, 0, 30}] (* G. C. Greubel, Sep 18 2018 *) nxt[{a_,b_,c_,d_}]:={b,c,d,(b*d+c^2)/a}; NestList[nxt,{1,2,4,16},20][[All,1]] (* Harvey P. Dale, Jul 28 2021 *) -
PARI
a(n)=if(n<4,[1,2,4,16][n+1],(a(n-1)*a(n-3)+a(n-2)^2)/a(n-4))
Formula
a(n) = 2^n*A006720(n+1) for all n in Z.
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