A344388 - OEIS

%I #23 Aug 17 2021 01:47:40

%S 1,0,5,7,4,7,3,5,9,6,1,0,2,9,3,0,7,1,4,5,8,8,3,6,1,3,6,9,0,1,1,1,7,2,

%T 1,2,3,2,5,9,5,6,8,3,4,0,4,0,1,4,9,4,6,9,5,1,9,6,0,0,8,8,9,3,4,0,8,4,

%U 1,4,1,8,9,2,9,2,5,7,3,5,3,8,4,8,5,1,2,6,6,6,7,6,0,5,3,3,5,1,0,5,5,3,4,0,1,9

%N Decimal expansion of a constant related to the asymptotics of A048634.

%C This constant is a very close to A201506.

%C Conjecture: It is equal to the limit of column "h^2" in the Table 1 in reference by Wright and Trefethen, p. 336.

%H T. G. Wright and L. N. Trefethen, <a href="http://dx.doi.org/10.1016/S0377-0427(00)00437-4">Computed Lyapunov constants for random recurrences with smooth coefficients</a>, J. Comp. Appl. Math. 132 (2) (2001), 331-340, Table 1.

%F Equals exp(limit_{n->infinity} log(A048634(n)) / A092526^n ).

%e 1.05747359610293071458836136901117212325956834040149469519600889340841418929257...

%t A092526 = 1/3 + 2/(3*(116 + 12*Sqrt[93])^(1/3)) + (1/6)*(116 + 12*Sqrt[93])^(1/3); terms = 500; b = ConstantArray[0, terms]; b[[7]] = N[Log[2], 1000]; b[[8]] = N[Log[3], 1000]; b[[9]] = N[Log[5], 1000]; Quiet[Do[b[[n]] = b[[n-1]] + b[[n-3]] - Sum[Exp[k*(b[[n-2]] - b[[n-1]] - b[[n-3]])]/k*(-1)^k, {k, 1, 1000}], {n, 10, terms}]; Exp[Table[N[b[[n]]/A092526^n, 110], {n, Length[b] - 20, Length[b]}]]]

%Y Cf. A048634, A092526, A201506.

%K nonn,cons

%O 1,3

%A _Vaclav Kotesovec_, Aug 16 2021