A184532 Array, read by rows: T(n,h)=floor[1/{(h+n^3)^(1/3)}], where h=1,2,...,3n^2+3n and {}=fractional part.

3, 2, 1, 1, 1, 1, 12, 6, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 13, 9, 7, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 48, 24, 16, 12, 9, 8, 7, 6, 5, 5, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 75, 37, 25, 18, 15, 12, 10, 9, 8, 7, 7, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1

Offset

1,1

Comments

(column 1)=A033428 (3n^2);

(column 2)=A184532=A000290+A007590;

(column 3)=A000290 (n^2);

(column 4)=A184534;

(column 5)=A184535;

(column 6)=A080476.

Links

Table of n, a(n) for n=1..162.

Formula

T(n,h)=floor[1/{(h+n^3)^(1/3)}], where h=1,2,...,3n^2+3n and {}=fractional part.

Example

First 2 rows:
3, 2, 1, 1, 1, 1
12, 6, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Mathematica

f[n_, h_]:=FractionalPart[(n^3+h)^(1/3)];
g[n_, h_]:=Floor[1/f[n, h]];
Table[Flatten[Table[g[n, h], {n, 1, 5}, {h, 1, 3n^2+3n}]]]
TableForm[Table[g[n, h], {n, 1, 5}, {h, 1, 3n^2+3n}]]

Crossrefs

Cf. A013942 (analogous array for sqrt(h+n^2), A184533

Sequence in context: A284997 A369367 A306709 * A016557 A073572 A073356

Adjacent sequences: A184529 A184530 A184531 * A184533 A184534 A184535

Keyword

nonn,tabf

Author

Clark Kimberling, Jan 16 2011

Status

approved