OFFSET
1,2
LINKS
Sela Fried, Proofs of some Conjectures from the OEIS, arXiv:2410.07237 [math.NT], 2024. See pp. 11-12.
FORMULA
Conjecture: a(n) = 2*a(n-2)+a(n-4)-2*a(n-6)-a(n-8) for n > 17. - Colin Barker, Oct 19 2014
Empirical g.f.: x*(x -1)*(40*x^15 +98*x^13 +4*x^11 +3*x^10 -80*x^9 +7*x^8 -2*x^6 -2*x^5 -12*x^4 -4*x^3 -4*x^2 -4*x -1) / (x^4 +x^2 -1)^2. - Colin Barker, Oct 19 2014
Conjecture: For n > 4, a(2*n+1) = A000045(n+3).
EXAMPLE
1/1 = 1 is a Fibonacci number. So a(1) = 1.
(1+2)/2 is not a Fibonacci number. (1+3)/2 = 2 is a Fibonacci number. So a(2) = 3.
(1+3+2)/3 = 2 is a Fibonacci number. So a(3) = 2.
PROG
(PARI) v=[]; n=1; while(n<10^7, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=1, n+2, if(fibonacci(i)>(num/(#v+1)), break); if(fibonacci(i)==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=1; break))); n++)
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Oct 18 2014
STATUS
approved