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A005255
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Atkinson-Negro-Santoro sequence: a(n+1) = 2a(n) - a(n-floor(n/2+1))
(Formerly M1076)
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2
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0, 1, 2, 4, 7, 13, 24, 46, 88, 172, 337, 667, 1321, 2629, 5234, 10444, 20842, 41638, 83188, 166288, 332404, 664636, 1328935, 2657533, 5314399, 10628131, 21254941, 42508561, 85014493, 170026357, 340047480, 680089726, 1360169008, 2720327572
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For each n, the n-term sequence (b(k) = a(n) - a(n-k), 1 <= k <= n), has the property that all 2^n sums of subsets of the terms are distinct.
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REFERENCES
| M. D. Atkinson et al., Sums of lexicographically ordered sets, Discrete Math., 80 (1990), 115-122.
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.28.
W. F. Lunnon, Integer sets with distinct subset-sums, Math. Comp., 50 (1988), 297-320.
T. V. Narayana, Recent progress and unsolved problems in dominance theory, pp. 68-78 of Combinatorial mathematics (Canberra 1977), Lect. Notes Math. Vol. 686, 1978.
T. V. Narayana, Lattice Path Combinatorics with Statistical Applications. Univ. Toronto Press, 1979, pp. 100-101.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..300
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EXAMPLE
| For n = 4, the sequence b is 7-4,7-2,7-1,7-0 = 3,5,6,7, which has subset sums (grouped by number of terms) 0, 3,5,6,7, 8,9,10,11,12,13, 14,15,16,18, 21.
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MATHEMATICA
| a[ 0 ] := 0; a[ 1 ] := 1; a[ n_ ] := 2*a[ n - 1 ] - a[(n - 1) - Floor[ (n - 1)/2 + 1 ] ]; For[ n = 1, n <= 100, n++, Print[ a[ n ] ] ];
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CROSSREFS
| Cf. A005318.
Sequence in context: A192675 A018185 A191526 * A086445 A127602 A113291
Adjacent sequences: A005252 A005253 A005254 * A005256 A005257 A005258
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 26 2000
Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 11 2009
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