OFFSET
0,4
COMMENTS
Farhi proved that a(n) > 0 for any n >= 0.
i^2/3 means (i^2)/3, of course, not i^(2/3). - N. J. A. Sloane, Feb 18 2019
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..10000
Bakir Farhi, An Elementary Proof that any Natural Number can be Written as the Sum of Three Terms of the Sequence floor(n^2/3), Journal of Integer Sequences, Vol. 17 (2014), #14.7.6.
Rémy Sigrist, PARI program for A306468
EXAMPLE
For n = 42:
- let f(k) = floor(k^2/3),
- 42 can be written in 5 ways as f(i) + f(j) + f(k) with 1 <= i <= j <= k:
f(1) + f(8) + f(8) = 0 + 21 + 21
f(2) + f(2) + f(11) = 1 + 1 + 40
f(2) + f(5) + f(10) = 1 + 8 + 33
f(3) + f(6) + f(9) = 3 + 12 + 27
f(4) + f(7) + f(8) = 5 + 16 + 21,
- hence a(42) = 5.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Feb 17 2019
STATUS
approved