OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) for n>=8.
G.f.: x*(x+1)*(x^5-2*x^4+x^3-2*x^2-2)/((x-1)^3*(x^2+x+1)). - Colin Barker, Oct 07 2012
a(n) = n^2 + floor(n^2/3) with n>2, a(1)=2, a(2)=6. This confirms the g.f. and the recurrence. - Bruno Berselli, Aug 08 2013
MATHEMATICA
p[n_]:=FractionalPart[(n^4+3*n)^(1/4)];
q[n_]:=Floor[1/p[n]];
Table[q[n], {n, 1, 80}]
FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
Join[{2, 6}, LinearRecurrence[{2, -1, 1, -2, 1}, {12, 21, 33, 48, 65}, 78]] (* Ray Chandler, Aug 02 2015 *)
PROG
(Magma) Fp:=func<i | Root(i^4+3*i, 4)-Iroot(i^4+3*i, 4)>; [Floor(1/Fp(n)): n in [1..80]]; // Bruno Berselli, Aug 08 2013
(PARI) x='x+O('x^30); Vec(x*(x+1)*(x^5-2*x^4+x^3-2*x^2-2)/((x-1)^3*(x^2 +x+1))) \\ G. C. Greubel, Apr 04 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 18 2011
STATUS
approved