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A165905 Somos-4 recurrence with a(0)=1, a(1)=2, a(2)=4, a(3)=16 1
1, 2, 4, 16, 48, 224, 1472, 7552, 80384, 782848, 8406016, 170625024, 2540736512, 64470204416, 2076557099008, 55281408770048, 3099925187854336, 147249506912960512, 8547656292050141184, 871531919951033532416 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
EXAMPLE
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
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 *)
PROG
(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))
(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
CROSSREFS
Sequence in context: A153951 A248748 A350646 * A104354 A153948 A284730
KEYWORD
nonn
AUTHOR
Jaume Oliver Lafont, Sep 29 2009
EXTENSIONS
"frac" keyword removed by Jaume Oliver Lafont, Oct 13 2009
STATUS
approved

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Last modified April 19 11:31 EDT 2024. Contains 371792 sequences. (Running on oeis4.)