0,3

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

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]

(PARI) a(n)=n^2\2

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

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.