OFFSET
0,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Cyril Banderier and Michael Wallner, Lattice paths with catastrophes, arXiv:1707.01931 [math.CO], 2017. See Corollary 4.22. on p. 24.
FORMULA
r = (sqrt(93)/18 + 1/2)^(1/3) - (sqrt(93)/18 - 1/2)^(1/3).
Constant r satisfies:
(1) 1/(1 - r*i) = (r + r^2*i) where i^2 = -1.
(2) r = real( 1/(1 - r*i) ).
(3) r = norm( 1/(1 - r*i) ).
(4) r = r^2 + r^4.
Equals 1/A092526. - Vaclav Kotesovec, Nov 27 2017
EXAMPLE
0.682327803828019327369483739711048256891188581897998577803728606639896...
MATHEMATICA
RealDigits[ ((Sqrt[93] + 9)/18)^(1/3) - ((Sqrt[93] - 9)/18)^(1/3), 10, 100][[1]] (* G. C. Greubel, May 01 2017 *)
PROG
(PARI) a(n) = my(r = (sqrt(93)/18 + 1/2)^(1/3) - (sqrt(93)/18 - 1/2)^(1/3)); floor(r*10^(n+1))%10
for(n=0, 120, print1(a(n), ", "))
(PARI) solve(r=0, 1, r^3 + r - 1 ) \\ Michel Marcus, Oct 25 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paul D. Hanna, Oct 24 2015
STATUS
approved