OFFSET
0,5
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 (terms 0..1000 from Alois P. Heinz)
Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian, Dyck paths with a first return decomposition constrained by height, Submitted, 2017.
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 2.50297436517909273228379630... and c = 0.34042564735836570861482... . - Vaclav Kotesovec, Aug 08 2016, updated Aug 27 2016
Conjecture: 1/d = 0.39952466709679946... = A268107. - Jean-François Alcover, Aug 08 2016
EXAMPLE
The sequence of polynomials is 0, x, x, x^2, x^2 + x, x^4 + x^3, x^4 + x^3 + x^2 + x, ..., and after this all the even polynomials end with x^3 + x^2 + x (+ 0), so the first 4 terms of the sequence are these coefficients (in ascending order): 0, 1, 1, 1. - Michael B. Porter, Aug 09 2016
MATHEMATICA
k = 32; P[0] = 0; P[1] = x;
P[n_] := P[n] = If[EvenQ[n], P[n-1] + P[n-2], P[n-1]*P[n-2]] + O[x]^(2k+1) // Normal;
CoefficientList[P[2k], x][[1 ;; k+1]] (* Jean-François Alcover, Aug 07 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
James Boudinot (jboudinot(AT)yahoo.com)
EXTENSIONS
More terms from Michael Somos, May 19 2000
STATUS
approved