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A008233 a(n) = floor(n/4)*floor((n+1)/4)*floor((n+2)/4)*floor((n+3)/4). 4
0, 0, 0, 0, 1, 2, 4, 8, 16, 24, 36, 54, 81, 108, 144, 192, 256, 320, 400, 500, 625, 750, 900, 1080, 1296, 1512, 1764, 2058, 2401, 2744, 3136, 3584, 4096, 4608, 5184, 5832, 6561, 7290, 8100, 9000, 10000, 11000, 12100, 13310, 14641, 15972, 17424, 19008, 20736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) is the maximal product of four nonnegative integers whose sum is n. - Andres Cicuttin, Sep 26 2018

REFERENCES

Mubayi, Dhruv. Counting substructures II: Hypergraphs, Combinatorica 33 (2013), no. 5, 591--612. MR3132928.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

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)

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 *)

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

Cf. A002620.

Sequence in context: A318654 A305656 A005943 * A224815 A031923 A304076

Adjacent sequences:  A008230 A008231 A008232 * A008234 A008235 A008236

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Stefan Steinerberger, Apr 03 2006

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)