OFFSET
1,3
COMMENTS
a(n+1) is the number of (finite) positive integer sequences b(1),...,b(k) with b(1) + Sum_{i=1..k-1} (1+max{b(i+1)-b(i), 0}) <= n. - Klaus Strassburger. [E.g., a(4)=8 since the integer sequences are 1; 2; 3; 1,1; 1,2; 2,1; 2,2; 1,1,1.]
FORMULA
G.f. (conjecture): 1 - G(0)/(1-x), where G(k)= 1 - 1/(1 - x/(1 - x/(1 - x/(1 - x/(x - 1/G(k+1)))))); (continued fraction). - Sergei N. Gladkovskii, Jul 12 2013
G.f. (conjecture): (2*x^3-x^2+2*x-1+sqrt(x^4+2*x^2-4*x+1))/(2*x^2-2*x). - Michael D. Weiner, Dec 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Sep 24 2001
More terms from Sean A. Irvine, Apr 10 2018
STATUS
approved