%I A005318 M1075
%S A005318 0,1,2,4,7,13,24,44,84,161,309,594,1164,2284,4484,8807,17305,34301,68008,
%T A005318 134852,267420,530356,1051905,2095003,4172701,8311101,16554194,
%U A005318 32973536,65679652,130828948,261127540,521203175,1040311347,2076449993
%N A005318 Conway-Guy sequence: a(n + 1) = 2a(n) - a(n - floor( 1/2 + sqrt(2n) )).
%C A005318 Conway and Guy conjecture that the set of k numbers {s_i = a(k) - a(k-i) 
               : 1 <= i <= k} has the property that all its subsets have distinct 
               sums - see Guy's book. These k-sets are the rows of A096858. [This 
               conjecture has apparently now been proved by Bohman. - I. Halupczok 
               (integerSequences(AT)karimmi.de), Feb 20 2006]
%D A005318 Tom Bohman: A sum packing problem of Erdos and the Conway-Guy sequence. 
               Proc. AMS 124, (No. 12, 1996), pp. 3627-3636.
%D A005318 P. Borwein and M. J. Mossinghoff, Newman Polynomials with Prescribed 
               Vanishing and Integer Sets with Distinct Subset Sums, Math. Comp., 
               72 (2003), 787-800.
%D A005318 J. H. Conway and R. K. Guy, Solution of a problem of Erdos, Colloq. Math. 
               20 (1969), p. 307.
%D A005318 R. K. Guy, Sets of integers whose subsets have distinct sums, pp. 141-154 
               of Theory and practice of combinatorics. Ed. A. Rosa, G. Sabidussi 
               and J. Turgeon. Annals of Discrete Mathematics, 12. North-Holland 
               1982.
%D A005318 R. K. Guy, Unsolved Problems in Number Theory, C8.
%D A005318 Kreweras, G.; Sur quelques problemes relatifs au vote pondere [Some problems 
               of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63.
%D A005318 G. Kreweras, Alvarez Rodriguez, Miguel-Angel; Ponderation entiere minimale 
               de N telle que pour tout k toutes les k-parties de N aient des poids 
               distincts. [Minimal integer weighting of N such that for any k all 
               the k-subsets of N have unequal weights] C. R. Acad. Sci. Paris Ser. 
               I Math. 296 (1983), no. 8, 345-347.
%D A005318 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005318 M. Wald, Problem 1192, Unequal sums, J. Rec. Math., 15 (No. 2, 1983-1984), 
               pp. 148-149.
%H A005318 T. D. Noe, <a href="b005318.txt">Table of n, a(n) for n=0..300</a>
%o A005318 (PARI) a(n)=if(n<=1,n==1,2*a(n-1)-a(n-1-(sqrtint(8*n-15)+1)\2))
%Y A005318 Cf. A037254, A096858, A096796, A096824.
%Y A005318 Sequence in context: A054175 A000073 A160254 this_sequence A102111 A059633 
               A088353
%Y A005318 Adjacent sequences: A005315 A005316 A005317 this_sequence A005319 A005320 
               A005321
%K A005318 nonn,easy,nice
%O A005318 0,3
%A A005318 N. J. A. Sloane (njas(AT)research.att.com).
%E A005318 More terms from Larry Reeves (larryr(AT)acm.org), Sep 21 2000