Search: id:A007590
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%I A007590 M1090
%S A007590 0,0,2,4,8,12,18,24,32,40,50,60,72,84,98,112,128,144,162,180,200,220,
%T A007590 242,264,288,312,338,364,392,420,450,480,512,544,578,612,648,684,722,
%U A007590 760,800,840,882,924,968,1012,1058,1104,1152,1200,1250,1300,1352,1404
%N A007590 Floor(n^2/2).
%C A007590 Arithmetic mean of a pair of successive triangular numbers. - Amarnath 
               Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005
%C A007590 Also the maximum sum of absolute values of differences of neighbors in 
               a cyclic permutation of 1..n. For example, with n = 9, many permutations 
               have a sum of 40, including 1 9 2 8 3 7 4 6 5: |1-9| + |9-2| + |2-8| 
               + |8-3| + |3-7| + |7-4| + |4-6| + |6-5| + |5-1| = 40. - Joshua Zucker 
               (joshua.zucker(AT)stanfordalumni.org), Dec 15 2005
%C A007590 It seems that a(n) = maximum number of non-overlapping 1x2 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 http://lagrange.ime.usp.br/
               ~lobato/packing/run/index.php [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), 
               Aug 03 2009]
%D A007590 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007590 T. D. Noe, <a href="b007590.txt">Table of n, a(n) for n=0..1000</a>
%H A007590 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A007590 a(n) = a(n-1)+a(n-2)-a(n-3)+2 = 2*A002620(n) = A000217(n+1)+A004526(n) 
               - Henry Bottomley (se16(AT)btinternet.com), Mar 08 2000
%F A007590 a(n+1) = Sum{k=1..n, k + mod(k,2)} for n >= 0. Therefore a(n) = Sum{k=1..n, 
               2*floor(k/2)} for n >= 0. - William A. Tedeschi (fynmun(AT)hotmail.com), 
               Mar 19 2008
%F A007590 G.f.: 2x^2/((1+x)(1-x)^3). a(n+1)-a(n)=A052928(n+1). [From R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Nov 22 2008]
%o A007590 (PARI) a(n)=n^2\2
%Y A007590 Column 3 of triangle A094953.
%Y A007590 For n>2: a(n) = sum of (n-1)-th row in triangle A101037.
%Y A007590 Cf. A000290, A000212, A118015, A056827, A118013.
%Y A007590 A080476 is essentially the same sequence.
%Y A007590 Sequence in context: A046843 A152125 A100057 this_sequence A080476 A053799 
               A085891
%Y A007590 Adjacent sequences: A007587 A007588 A007589 this_sequence A007591 A007592 
               A007593
%K A007590 nonn,easy
%O A007590 0,3
%A A007590 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.

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