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Search: id:A005230
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| A005230 |
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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).
(Formerly M0785)
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+0
7
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| 1, 1, 2, 3, 6, 11, 20, 40, 77, 148, 285, 570, 1120, 2200, 4323, 8498, 16996, 33707, 66844, 132568, 262936, 521549, 1043098, 2077698, 4138400, 8243093, 16419342, 32706116, 65149296, 130298592, 260075635, 519108172, 1036138646, 2068138892, 4128034691
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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Kreweras, G.; Sur quelques problemes relatifs au vote pondere, [ Some problems of weighted voting ] Math. Sci. Humaines No. 84 (1983), 45-63.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. A. Stern, Aufgaben, J. Reine Angew. Math., 18 (1838), 100.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..200
Index entries for sequences related to Stern's sequences
Index entries for "core" sequences
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FORMULA
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Partial sums give Conway-Guy sequence A005318. Cf. A066777.
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
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MAPLE
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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)];
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PROGRAM
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(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
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CROSSREFS
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Sequence in context: A141435 A096080 A143658 this_sequence A030037 A077078 A077079
Adjacent sequences: A005227 A005228 A005229 this_sequence A005231 A005232 A005233
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KEYWORD
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core,easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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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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