|
|
A111459
|
|
Generalized Somos-4 sequence with a(n-2)^2 replaced by a(n-2)^5.
|
|
3
|
|
|
1, 1, 1, 1, 2, 3, 35, 313, 26261407, 1001689887346, 356879751557595054813966522072161803, 3221974575788016845202611315068840860244866942009716269469
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (a(n-1)*a(n-3) + a(n-2)^5)/a(n-4) for n >= 4 with a(0) = a(1) = a(2) = a(3) = 1. As n tends to infinity, log(log(a(n)))/n tends to (1/2)*log((5 + sqrt(21))/2) or about 0.783.
|
|
MAPLE
|
L[0]:=0; L[1]:=0; L[2]:=0; L[3]:=0; for n from 0 to 4000 do L[n+4]:=evalf(ln(1+exp(L[n+3]+L[n+1]-5*L[n+2]))+5*L[n+2]-L[n]): od: for n from 3990 to 4000 do print(evalf(ln(L[n+4])/(n+4))): od: #Note: this calculates L[n]=ln(a[n]) and illustrates slow convergence of ln(ln(a[n]))/n to 0.783...
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|