A111459 Generalized Somos-4 sequence with a(n-2)^2 replaced by a(n-2)^5.
1, 1, 1, 1, 2, 3, 35, 313, 26261407, 1001689887346, 356879751557595054813966522072161803, 3221974575788016845202611315068840860244866942009716269469
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..14
- S. Fomin and A. Zelevinsky, The Laurent Phenomenon, Advances in Applied Mathematics 28 (2002), 119-144.
- D. Gale, Tracking the Automatic Ant, Springer (1998), pp. 1-5.
- D. Gale, The strange and surprising saga of the Somos sequences, Math. Intelligencer 13(1) (1991), pp. 40-42.
- D. Gale, Somos sequence update, Mathematical Intelligencer 13 (4) (1991), 49-50.
Programs
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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...
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.