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A047838
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Floor(n^2/2)-1.
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8
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1, 3, 7, 11, 17, 23, 31, 39, 49, 59, 71, 83, 97, 111, 127, 143, 161, 179, 199, 219, 241, 263, 287, 311, 337, 363, 391, 419, 449, 479, 511, 543, 577, 611, 647, 683, 721, 759, 799, 839, 881, 923, 967, 1011, 1057, 1103, 1151, 1199, 1249, 1299, 1351, 1403
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Define the organization number of a permutation pi_1, pi_2, ..., pi_n to be the following. Start at 1, count the steps to reach 2, then the steps to reach 3, etc. Add them up. Then the maximal value of the organization number of any permutation of [1..n] for n = 0, 1, 2, 3, ... is given by 0, 1, 3, 7, 11, 17, 23, ... (this sequence). This was established by Graham Cormode (graham(AT)research.att.com), Aug 17 2006, see link below, answering a question raised by Tom Young (mcgreg265(AT)msn.com) and Barry Cipra, Aug 15 2006.
Comment from Dmitry Kamenetsky (Dmitry.Kamenetsky(AT)rsise.anu.edu.au), Nov 29 2006: This is the length of the longest non self-intersecting spiral drawn on an N X N grid. E.g. for n=5 the spiral has length 17:
10111
10101
10101
10001
11111
It appears that a(n+1) is the maximum number of consecutive integers (beginning with 1) that can be placed, one after another, on an n-peg Towers of Hanoi, such that the sum of any two consecutive integers on any peg is a square. See the problem: http://online-judge.uva.es/p/v102/10276.html [From Ashutosh Mehra (ashutoshmehra(AT)gmail.com), Dec 06 2008]
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LINKS
| Graham Cormode, Notes on the organization number of a permutation.
Index to sequences with linear recurrences with constant coefficients, signature (2,0,-2,1).
Reinhard Zumkeller, Table of n, a(n) for n = 2..10000
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FORMULA
| a(2)=1; for n>2, a(n) = a(n-1)+n-1+(n-1 mod 2). - Benoit Cloitre, Jan 12 2003
T(n-1)+floor(n/2)-1 = T(n)-floor((n+3)/2), where T(n) is the n-th triangular number (A000217). - Robert G. Wilson v, Aug 31 2006.
Equals (n-1)-th row sums of triangles A134151 and A135152. Also, = binomial transform of [1, 2, 2, -2, 4, -8, 16, -32,...]. - Gary W. Adamson, Nov 21 2007
G.f.: x^2(1+x+x^2-x^3)/((1-x)^3*(1+x)). - R. J. Mathar, Sep 09 2008
a(n) = floor((n^2+4*n+2)/2). - Gary Detlefs, Feb 10 2010
a(n) = abs(A188653(n)). - Reinhard Zumkeller, Apr 13 2011
a(n) = (2*n^2+(-1)^n-5)/4. - Bruno Berselli, Sep 14 2011
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MAPLE
| seq(floor((n^2+4*n+2)/2), n=0..20) [From Gary Detlefs, Feb 10 2010]
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MATHEMATICA
| Table[ Floor[n^2/2] - 1, {n, 2, 60}] (* Robert G. Wilson v, Aug 31 2006 *)
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PROG
| (PARI) a(n)=n^2\2-1
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CROSSREFS
| Complement of A047839. Also A007590 - 1. First differences give A052928.
Cf. A135151, A135152.
Sequence in context: A184856 A023234 A134707 * A188653 A180452 A029715
Adjacent sequences: A047835 A047836 A047837 * A047839 A047840 A047841
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KEYWORD
| nonn,easy
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AUTHOR
| Michael Somos
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EXTENSIONS
| Edited by Charles R Greathouse IV, Apr 23 2010
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