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A118015 a(n) = floor(n^2/5). 19
0, 0, 0, 1, 3, 5, 7, 9, 12, 16, 20, 24, 28, 33, 39, 45, 51, 57, 64, 72, 80, 88, 96, 105, 115, 125, 135, 145, 156, 168, 180, 192, 204, 217, 231, 245, 259, 273, 288, 304, 320, 336, 352, 369, 387, 405, 423, 441, 460, 480, 500, 520, 540, 561, 583, 605, 627, 649, 672 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
It seems that for n >= 5, a(n) is the maximum number of non-overlapping 1 X 5 rectangles that can be packed into an n X n square. Rectangles can only be placed parallel to the sides of the square. Verified with Lobato's program. - Dmitry Kamenetsky, Aug 03 2009
LINKS
FORMULA
G.f.: x^3*(1 + x)/((1 + x + x^2 + x^3 + x^4)*(1 - x)^3). - Klaus Brockhaus, Nov 18 2008
a(n) = A008732(n-4) + A008732(n-3). - R. J. Mathar, Nov 22 2008
a(5*m+r) = m*(5*m + 2*r) + a(r), with m >= 0 and 0 <= r < 5. Example: for m=4 and r=3, a(5*4+3) = a(23) = 4*(5*4 + 2*3) + a(3) = 104 + 1 = 105. - Bruno Berselli, Dec 12 2016
Sum_{n>=3} 1/a(n) = 25/16 + Pi^2/30 + sqrt(5-2*sqrt(5))*Pi/4. - Amiram Eldar, Aug 13 2022
MATHEMATICA
Table[Floor[n^2/5], {n, 0, 60}] (* Bruno Berselli, Dec 12 2016 *)
PROG
(Magma) [ n^2 div 5: n in [0..58] ]; // Klaus Brockhaus, Nov 18 2008
(PARI) a(n)=n^2\5 \\ Charles R Greathouse IV, Sep 24 2015
(Python) [int(n**2/5) for n in range(60)] # Bruno Berselli, Dec 12 2016
(Sage) [floor(n^2/5) for n in range(60)] # Bruno Berselli, Dec 12 2016
CROSSREFS
Sequence in context: A333601 A316312 A362128 * A265057 A122643 A194240
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Apr 10 2006
EXTENSIONS
Edited by Charles R Greathouse IV, Apr 20 2010
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)