Search: id:A005230
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%I A005230 M0785
%S A005230 1,1,2,3,6,11,20,40,77,148,285,570,1120,2200,4323,8498,16996,33707,66844,
%T A005230 132568,262936,521549,1043098,2077698,4138400,8243093,16419342,32706116,
%U A005230 65149296,130298592,260075635,519108172,1036138646,2068138892,4128034691
%N A005230 Stern's sequence: a(1) = 1, a(n+1) is the sum of the m preceding terms, 
               where m*(m-1)/2 < n <= m*(m+1)/2 or equivalently m = ceil((sqrt(8*n+1)-1)/
               2) = A002024(n).
%D A005230 Kreweras, G.; Sur quelques problemes relatifs au vote pondere, [ Some 
               problems of weighted voting ] Math. Sci. Humaines No. 84 (1983), 
               45-63.
%D A005230 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005230 M. A. Stern, Aufgaben, J. Reine Angew. Math., 18 (1838), 100.
%H A005230 T. D. Noe, <a href="b005230.txt">Table of n, a(n) for n = 1..200</a>
%H A005230 <a href="Sindx_St.html#Stern">Index entries for sequences related to 
               Stern's sequences</a>
%H A005230 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A005230 Partial sums give Conway-Guy sequence A005318. Cf. A066777.
%F A005230 2*a(n*(n+1)/2 + 1) = a(n*(n+1)/2 + 2) for n>=1; limit_{n->infty} a(n+1)/
               a(n) = 2. - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 28 2006
%p A005230 A005230[1] := 1: n := 50: for k from 1 to n-1 do: A005230[k+1] := sum('A005230[j]',
               'j'=k+1-(ceil((sqrt(8*k+1)-1)/2))..k): od: [seq(A005230[k],k=1..n)];
%o A005230 (PARI) a(n)=if(n==1,1,sum(k=1,ceil((sqrt(8*n-7)-1)/2),a(n-k))) - Paul 
               D. Hanna (pauldhanna(AT)juno.com), Aug 28 2006
%Y A005230 Sequence in context: A141435 A096080 A143658 this_sequence A030037 A077078 
               A077079
%Y A005230 Adjacent sequences: A005227 A005228 A005229 this_sequence A005231 A005232 
               A005233
%K A005230 core,easy,nonn,nice
%O A005230 1,3
%A A005230 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005230 Description corrected by Mario Szegedy Sep 15 1996; and revised with 
               Maple code by UlrSchimke(AT)aol.com, Mar 16, 2002

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