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A064790
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Inverse permutation to A060734.
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4
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1, 3, 5, 2, 6, 9, 13, 8, 4, 10, 14, 19, 25, 18, 12, 7, 15, 20, 26, 33, 41, 32, 24, 17, 11, 21, 27, 34, 42, 51, 61, 50, 40, 31, 23, 16, 28, 35, 43, 52, 62, 73, 85, 72, 60, 49, 39, 30, 22, 36, 44, 53, 63, 74, 86, 99, 113, 98, 84, 71, 59, 48, 38, 29, 45, 54, 64, 75, 87, 100, 114
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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From Boris Putievskiy, Mar 14 2013: (Start)
a(n) is a pairing function: a function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} is the set of integer positive numbers.
Layer is pair of sides of square from T(1,n) to T(n,n) and from T(n,n) to T(n,1). This sequence is A188568 as table read by boustrophedonic ("ox-plowing") method - layer clockwise, layer counterclockwise and so. The same table A188568 read layer by layer clockwise is A194280. (End)
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LINKS
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Table of n, a(n) for n=1..71.
Index entries for sequences that are permutations of the natural numbers
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO]
Eric Weisstein's MathWorld, Pairing Function
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FORMULA
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a(n) = (i+j-1)*(i+j-2)/2+i, where i=min(t; t^2-n+1), j=min(t; n-(t-1)^2), t=floor(sqrt(n-1))+1. - Boris Putievskiy, Dec 24 2012
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EXAMPLE
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From Boris Putievskiy, Mar 14 2013: (Start)
The start of the sequence as table:
1....2...6...7..15..16..28...
3....5...9..12..20..23..35...
4....8..13..18..26..31..43...
10..14..19..25..33..40..52...
11..17..24..32..41..50..62...
21..27..34..42..51..61..73...
22..30..39..49..60..72..85...
. . .
The start of the sequence as triangular array read by rows:
1;
3,5,2;
6,9,13,8,4;
10,14,19,25,18,12,7;
15,20,26,33,41,32,24,17,11;
21,27,34,42,51,61,50,40,31,23,16;
28,35,43,52,62,73,85,72,60,49,39,30,22;
. . .
Row number r contains 2*r-1 numbers. (End)
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CROSSREFS
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Cf. A060734, A064788, A188568, A194280.
Sequence in context: A010782 A333111 A139584 * A113966 A164611 A316086
Adjacent sequences: A064787 A064788 A064789 * A064791 A064792 A064793
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Oct 20 2001
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STATUS
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approved
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