A184534 a(n) = floor(1/{(4+n^3)^(1/3)}), where {}=fractional part.

1, 3, 7, 12, 18, 27, 36, 48, 60, 75, 90, 108, 126, 147, 168, 192, 216, 243, 270, 300, 330, 363, 396, 432, 468, 507, 546, 588, 630, 675, 720, 768, 816, 867, 918, 972, 1026, 1083, 1140, 1200, 1260, 1323, 1386, 1452, 1518, 1587, 1656, 1728, 1800, 1875, 1950, 2028, 2106, 2187, 2268, 2352, 2436, 2523, 2610, 2700, 2790, 2883, 2976, 3072, 3168, 3267, 3366, 3468, 3570, 3675, 3780, 3888, 3996, 4107, 4218, 4332, 4446, 4563, 4680, 4800, 4920, 5043, 5166, 5292, 5418, 5547, 5676, 5808

Offset: 1

Author

Clark Kimberling, Jan 16 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A183532, A183534.

Programs

Mathematica

Table[Floor[1/FractionalPart[(n^3 + 4)^(1/3)]], {n, 1, 120}]

PARI

for(n=1, 50, print1(floor(1/frac((4 + n^3)^(1/3))), ", ")) \\ G. C. Greubel, May 14 2017

Formula

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

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

From Colin Barker, Oct 07 2012: (Start)

Empirical: a(n) = 3*(1 - (-1)^n + 4*n + 2*n^2)/8 for n>2.

Empirical G.f.: x*(x^6-2*x^5+x^4-x^2-x-1)/((x-1)^3*(x+1)).(End)