A344388 Decimal expansion of a constant related to the asymptotics of A048634.

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, 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, 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

Offset

1,3

Comments

This constant is a very close to A201506.

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

Links

Table of n, a(n) for n=1..106.

T. G. Wright and L. N. Trefethen, Computed Lyapunov constants for random recurrences with smooth coefficients, J. Comp. Appl. Math. 132 (2) (2001), 331-340, Table 1.

Formula

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

Example

1.05747359610293071458836136901117212325956834040149469519600889340841418929257...

Mathematica

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]}]]]

Crossrefs

Cf. A048634, A092526, A201506.

Sequence in context: A343039 A021178 A201506 * A198985 A021639 A232975

Adjacent sequences: A344385 A344386 A344387 * A344389 A344390 A344391

Keyword

nonn,cons

Author

Vaclav Kotesovec, Aug 16 2021

Status

approved