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 A005255 Atkinson-Negro-Santoro sequence: a(n+1) = 2a(n) - a(n-floor(n/2+1)). (Formerly M1076) 6
 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; text; internal format)
 OFFSET 0,3 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. a(n) = A062178(n+1) - 1; see also A002083. - Reinhard Zumkeller, Nov 18 2012 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.28. 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). LINKS T. D. Noe, Table of n, a(n) for n=0..300 M. D. Atkinson et al., Sums of lexicographically ordered sets, Discrete Math., 80 (1990), 115-122. W. F. Lunnon, Integer sets with distinct subset-sums, Math. Comp. 50 (1988), 297-320. B. E. Wynne & N. J. A. Sloane, Correspondence, 1976-84 B. E. Wynne & T. V. Narayana, Tournament configuration, weighted voting, and partitioned catalans, Preprint. Bayard Edmund Wynne, and T. V. Narayana, Tournament configuration and weighted voting, Cahiers du bureau universitaire de recherche opérationnelle, 36 (1981): 75-78. 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. 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 ] ] ]; PROG (Haskell) a005255 n = a005255_list !! (n-1) a005255_list = scanl (+) 0 \$ tail a002083_list -- Reinhard Zumkeller, Nov 18 2012 CROSSREFS Cf. A002083, A005318, A062178. Sequence in context: A192675 A018185 A191526 * A086445 A127602 A113291 Adjacent sequences:  A005252 A005253 A005254 * A005256 A005257 A005258 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 26 2000 Edited by Franklin T. Adams-Watters, Apr 11 2009 STATUS approved

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Last modified October 20 04:37 EDT 2018. Contains 316378 sequences. (Running on oeis4.)