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%I #18 May 12 2019 19:09:50
%S 1,1,1,1,2,3,35,313,26261407,1001689887346,
%T 356879751557595054813966522072161803,
%U 3221974575788016845202611315068840860244866942009716269469
%N Generalized Somos-4 sequence with a(n-2)^2 replaced by a(n-2)^5.
%H Seiichi Manyama, <a href="/A111459/b111459.txt">Table of n, a(n) for n = 0..14</a>
%H S. Fomin and A. Zelevinsky, <a href="http://dx.doi.org/10.1006/aama.2001.0770">The Laurent Phenomenon</a>, Advances in Applied Mathematics 28 (2002), 119-144.
%H D. Gale, <a href="http://www.amazon.com/gp/reader/0387982728/ref=sib_dp_pt/103-2268091-4647057#reader-link">Tracking the Automatic Ant</a>, Springer (1998), pp. 1-5.
%H D. Gale, <a href="http://dx.doi.org/10.1007/BF03024070">The strange and surprising saga of the Somos sequences</a>, Math. Intelligencer 13(1) (1991), pp. 40-42.
%H D. Gale, <a href="http://dx.doi.org/10.1007/BF03028343">Somos sequence update</a>, Mathematical Intelligencer 13 (4) (1991), 49-50.
%F 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.
%p 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...
%Y Cf. A006720, A072876, A072877.
%K nonn
%O 0,5
%A _Andrew Hone_, Nov 15 2005
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