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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.
2
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.
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
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Jan 16 2011
STATUS
approved