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.
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
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