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Search: id:A007590
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| A007590 |
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Floor(n^2/2).
(Formerly M1090)
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+0
21
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| 0, 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, 128, 144, 162, 180, 200, 220, 242, 264, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 722, 760, 800, 840, 882, 924, 968, 1012, 1058, 1104, 1152, 1200, 1250, 1300, 1352, 1404
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Arithmetic mean of a pair of successive triangular numbers. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005
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
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]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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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
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
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]
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PROGRAM
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(PARI) a(n)=n^2\2
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CROSSREFS
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Column 3 of triangle A094953.
For n>2: a(n) = sum of (n-1)-th row in triangle A101037.
Cf. A000290, A000212, A118015, A056827, A118013.
A080476 is essentially the same sequence.
Sequence in context: A046843 A152125 A100057 this_sequence A080476 A053799 A085891
Adjacent sequences: A007587 A007588 A007589 this_sequence A007591 A007592 A007593
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.
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