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Search: id:A062178
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| A062178 |
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a(n+1) = 2a(n)-a([n/2]) starting with a(0)=0 and a(1)=1. |
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2
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| 0, 1, 2, 3, 5, 8, 14, 25, 47, 89, 173, 338, 668, 1322, 2630, 5235, 10445, 20843, 41639, 83189, 166289, 332405, 664637, 1328936, 2657534, 5314400, 10628132, 21254942, 42508562, 85014494, 170026358, 340047481, 680089727, 1360169009, 2720327573
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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As partial sum of Narayana-Zidek-Capell numbers A002083, this is the number of words beginning with 1, with sum of integers <=n, in the sequence 1, 11, 111, 112, 1111, 1112, 1113, 1121, 1122, 1123, 1124, 11111, 11112, 11113, 11114, 11121, 11122, 11123, 11124, 11125, 11131, 11132, 11133, 11134, 11135, 11136, where any positive integer, in any word, is <= the sum of the preceding integers.
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FORMULA
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a(n) =a(n-1)+A002083(n).
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EXAMPLE
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a(7)=2a(6)-a(3)=2*14-3=25. a(8)=2a(7)-a(3)=2*25-3=47. a(9)=2a(8)-a(4)=2*47-5=89.
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CROSSREFS
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Sequence in context: A036241 A125028 A119262 this_sequence A065955 A104880 A152478
Adjacent sequences: A062175 A062176 A062177 this_sequence A062179 A062180 A062181
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 12 2001
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