OFFSET
0,6
COMMENTS
a(n) is the maximal product of four nonnegative integers whose sum is n. - Andres Cicuttin, Sep 26 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Dhruv Mubayi, Counting substructures II: Hypergraphs, preprint, 2012.
Dhruv Mubayi, Counting substructures II: Hypergraphs, Combinatorica 33 (2013), no. 5, 591--612. MR3132928.
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,3,-6,3,0,-3,6,-3,0,1,-2,1).
FORMULA
Let b(n) = A002620(n), the quarter-squares. Then this sequence is b(0)*b(0), b(0)*b(1), b(1)*b(1), b(1)*b(2), b(2)*b(2), b(2)*b(3), ...
From R. J. Mathar, Feb 20 2011: (Start)
a(n) = 2*a(n-1) - a(n-2) + 3*a(n-4) - 6*a(n-5) + 3*a(n-6) - 3*a(n-8) + 6*a(n-9) - 3*a(n-10) + a(n-12) - 2*a(n-13) + a(n-14).
G.f.: -x^4*(1+x^6+x^2+2*x^3+x^4) / ( (1+x)^3*(x^2+1)^3*(x-1)^5 ). (End)
Sum_{n>=4} 1/a(n) = 1 + zeta(4). - Amiram Eldar, Jan 10 2023
a(4*n) = n^4. - Bernard Schott, Jan 24 2023
MAPLE
A008233:=n->floor(n/4)*floor((n+1)/4)*floor((n+2)/4)*floor((n+3)/4); seq(A008233(n), n=0..50); # Wesley Ivan Hurt, Dec 31 2013
MATHEMATICA
Table[Floor[n/4]*Floor[(n + 1)/4]*Floor[(n + 2)/4]*Floor[(n + 3)/4], {n, 0, 50}] (* Stefan Steinerberger, Apr 03 2006 *)
Table[Times@@Floor[Range[n, n+3]/4], {n, 0, 50}] (* Harvey P. Dale, Mar 30 2019 *)
PROG
(Haskell)
a008233 n = product $ map (`div` 4) [n..n+3]
-- Reinhard Zumkeller, Jun 08 2011
(Magma) [Floor(n/4)*Floor((n+1)/4)*Floor((n+2)/4)*Floor((n+3)/4): n in [0..50]]; // Vincenzo Librandi, Jun 09 2011
(PARI) a(n) = prod(i=0, 3, (n+i)\4); \\ Altug Alkan, Sep 27 2018
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Stefan Steinerberger, Apr 03 2006
STATUS
approved