OFFSET
1,2
LINKS
Edward Jiang and Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Edward Jiang)
Index entries for linear recurrences with constant coefficients, signature (3, -3, 2, -3, 3, -1).
FORMULA
a(n) = floor(1/{(9+n^4)^(1/4)}), where {} = fractional part.
It appears that a(n) = 3a(n-1)-3a(n-2)+2a(n-3)-3a(n-4)+3a(n-5)-a(n-6) for n>=9.
Empirical g.f.: x*(x+1)*(x^6-3*x^5+3*x^4-x^3+3*x^2+1) / ((x-1)^4*(x^2+x+1)). - Colin Barker, Jun 13 2015
MATHEMATICA
p[n_]:=FractionalPart[(n^4+9)^(1/4)]; q[n_]:=Floor[1/p[n]];
Table[q[n], {n, 1, 80}]
FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
Join[{1, 4}, LinearRecurrence[{3, -3, 2, -3, 3, -1}, {12, 28, 55, 96, 152, 227}, 73]] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) a(n)=my(t=(9+n^4)^(1/4)); 1\(t-t\1) \\ Charles R Greathouse IV, Sep 12 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 18 2011
STATUS
approved