OFFSET
0,2
COMMENTS
a(n+3) = maximal product of three numbers with sum n: a(n) = max(r*s*t), n = r+s+t. - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003
It appears that k is a term of the sequence if and only if k is a positive integer such that floor(v) * ceiling(v) * round(v) = k, where v = k^(1/3). - John W. Layman, Mar 21 2012
The sequence floor(n/3)*floor((n+1)/3)*floor((n+2)/3) is essentially the same: 0, 0, 0, 1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 80, 100, 125, 150, 180, 216, 252, ... - N. J. A. Sloane, Dec 27 2013
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
G. E. Bergum and V. E. Hoggatt, Jr., A combinatorial problem involving recursive sequences and tridiagonal matrices, Fib. Quart., 16 (1978), 113-118.
Dhruv Mubayi, Counting substructures II: Hypergraphs, Combinatorica 33 (2013), no. 5, 591--612. MR3132928.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).
FORMULA
a(n) = [(n+3)/3] * [(n+4)/3] * [(n+5)/3]. - Reinhard Zumkeller, May 18 2004
a(n-3) = Sum_{k=0..n} [k/3]*[(k+1)/3]. - Mitch Harris, Dec 02 2004
Sum_{n>=0} 1/a(n) = 1 + zeta(3). - Amiram Eldar, Jan 10 2023
a(3*m) = (m+1)^3 (A000578). - Bernard Schott, Feb 22 2023
MAPLE
A006501:=(1+z**2)/(z**2+z+1)**2/(z-1)**4; # Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[(1+x^2)/(1-x)^2 /(1-x^3)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 16 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Reinhard Zumkeller, May 18 2004
STATUS
approved