A184637 a(n) = floor(1/{(n^4+3*n)^(1/4)}), where {}=fractional part.

2, 6, 12, 21, 33, 48, 65, 85, 108, 133, 161, 192, 225, 261, 300, 341, 385, 432, 481, 533, 588, 645, 705, 768, 833, 901, 972, 1045, 1121, 1200, 1281, 1365, 1452, 1541, 1633, 1728, 1825, 1925, 2028, 2133, 2241, 2352, 2465, 2581, 2700, 2821, 2945, 3072, 3201, 3333, 3468, 3605, 3745, 3888, 4033, 4181, 4332, 4485, 4641, 4800, 4961, 5125, 5292, 5461, 5633, 5808, 5985, 6165, 6348, 6533, 6721, 6912, 7105, 7301, 7500, 7701, 7905, 8112, 8321, 8533

Offset: 1

Author

Clark Kimberling, Jan 18 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A184535, A184636.

Programs

Magma

Fp:=func; [Floor(1/Fp(n)): n in [1..80]]; // 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 *)

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

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