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A322633 Decimal expansion of the real solution to 11571875*x^5 - 5363750*x^4 + 628250*x^3 - 97580*x^2 + 5180*x - 142 = 0, multiplied by 3/7. Constant occurring in the asymptotic behavior of the number of lattice paths of slope 2/5, observed by D. Knuth. 2
1, 5, 8, 6, 6, 8, 2, 2, 6, 9, 7, 2, 0, 2, 2, 7, 7, 5, 5, 1, 4, 7, 8, 0, 4, 1, 9, 8, 1, 6, 3, 9, 2, 7, 3, 9, 2, 0, 6, 3, 7, 3, 7, 5, 7, 5, 5, 3, 0, 6, 6, 9, 7, 7, 9, 6, 3, 6, 6, 5, 2, 4, 0, 9, 5, 4, 4, 0, 7, 6, 7, 0, 2, 1, 0, 9, 5, 3, 1, 2, 5, 7, 9, 6, 1, 9, 1, 7, 1, 9, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
In his 2014 lecture in Paris "Problems That Philippe (Flajolet) Would Have Loved" D. Knuth discussed as Problem 4 "Lattice Paths of Slope 2/5" and reported as an empirical observation that A[5*t-1,2*t-1]/B[5*t-1,2*t-1] = a - b/t + O(t^-2), with constants a~=1.63026 and b~=0.159. For the meaning of A and B see A322631. The exact values of a (A322632) and b (this sequence) were found in 2016 by Banderier and Wallner.
LINKS
Cyril Banderier, Michael Wallner, Lattice paths of slope 2/5, arXiv:1605.02967 [cs.DM], 10 May 2016.
Don E. Knuth, Problems That Philippe Would Have Loved, Paris 2014.
EXAMPLE
0.1586682269720227755147804198163927392063737575530669779636652409544...
MAPLE
evalf[100]((3/7)*solve(11571875*x^5 -5363750*x^4 +628250*x^3 -97580*x^2 +5180*x -142=0, x)[1]); # Muniru A Asiru, Dec 21 2018
PROG
(PARI) (3/7)*solve(x=0, 1, 11571875*x^5 -5363750*x^4 +628250*x^3 -97580*x^2 +5180*x -142)
CROSSREFS
Sequence in context: A301862 A245944 A160043 * A346443 A145432 A335565
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Dec 21 2018
STATUS
approved

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Last modified March 29 22:15 EDT 2024. Contains 371282 sequences. (Running on oeis4.)