

A118015


a(n) = floor(n^2/5).


15



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
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OFFSET

0,5


COMMENTS

It seems that for n>=5, a(n) = maximum number of nonoverlapping 1x5 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

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
R. D. Lobato, Recursive partitioning approach for the Manufacturer's Pallet Loading Problem
Index entries for linear recurrences with constant coefficients, signature (2,1,0,0,1,2,1).


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(n4) + A008732(n3).  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


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 xrange(60)] # Bruno Berselli, Dec 12 2016
(Sage) [floor(n^2/5) for n in xrange(60)] # Bruno Berselli, Dec 12 2016


CROSSREFS

Cf. A000212, A000290, A007590, A002620, A056827, A118013, A279169.
Sequence in context: A226332 A226331 A316312 * A265057 A122643 A194240
Adjacent sequences: A118012 A118013 A118014 * A118016 A118017 A118018


KEYWORD

nonn,easy


AUTHOR

Reinhard Zumkeller, Apr 10 2006


EXTENSIONS

Edited by Charles R Greathouse IV, Apr 20 2010


STATUS

approved



