|
Search: id:A111459
|
|
|
| A111459 |
|
Generalized Somos-4 sequence with a(n-2)^2 replaced by a(n-2)^5. |
|
+0
1
|
|
| 1, 1, 1, 1, 2, 3, 35, 313, 26261407, 1001689887346, 356879751557595054813966522072161803, 3221974575788016845202611315068840860244866942009716269469
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
REFERENCES
|
D. Gale, The strange and surprising saga of the Somos sequences, Mathematical Intelligencer 13 (1) (1991), 40-42; Somos sequence update, Mathematical Intelligencer 13 (4) (1991), 49-50.
S. Fomin and A. Zelevinsky, The Laurent Phenomenon, Adv. Appl. Math. 28 (2002) 119-144.
|
|
LINKS
|
D. Gale, Tracking the Automatic Ant, Springer (1998) pp. 1-5.
|
|
FORMULA
|
a(n) = (a(n-1)*a(n-3)+a(n-2)^5)/a(n-4), 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
|
Cf. A006720, A072876, A072877.
Sequence in context: A143887 A141503 A165448 this_sequence A042663 A072291 A084191
Adjacent sequences: A111456 A111457 A111458 this_sequence A111460 A111461 A111462
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Andrew Hone (anwh(AT)kent.ac.uk), Nov 15 2005
|
|
|
Search completed in 0.002 seconds
|
