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Search: id:A005257
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| A005257 |
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Number of weighted voting procedures.
(Formerly M0716)
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+0
1
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| 2, 3, 5, 9, 17, 33, 64, 126, 249, 495, 984, 1962, 3913, 7815, 15608, 31194, 62346, 124650, 249216, 498348, 996531, 1992897, 3985464, 7970598, 15940542, 31880430, 63759552, 127517796, 255032987, 510063369, 1020121528, 2040237846, 4080465294, 8160920190
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Appears to satisfy a(1)=2, a(2)=3, a(3)=5 and, for n>3, a(n)=3a(n-1)-2a(n-2) if n is even and a(n)=a(n-1)+2a(n-2)-a([(n-1)/2]-1) if n is odd - John W. Layman (layman(AT)math.vt.edu), Jan 10 2000.
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REFERENCES
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G. Kreweras, Sur quelques problemes relatifs au vote pondere [Some problems of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63.
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).
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MATHEMATICA
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a={2, 3, 5}; For[i=4, i<35, i++, If[EvenQ[i], a=Append[a, 3 a[[i-1]]-2a[[i-2]]], a=Append[a, a[[i-1]]+2a[[i-2]]-a[[(i-1)/2-1]]]]]; a
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CROSSREFS
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Sequence in context: A080889 A049858 A092483 this_sequence A091697 A109740 A000051
Adjacent sequences: A005254 A005255 A005256 this_sequence A005258 A005259 A005260
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 20 2002
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