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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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4
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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
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OFFSET
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0,3
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COMMENTS
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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.
The subsequence of primes in this partial sum begins: 2, 3, 5, 47, 89, 173, 166289. [From Jonathan Vos Post, Feb 17 2010]
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LINKS
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FORMULA
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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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PROG
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(Haskell)
a062178 n = a062178_list !! (n-1)
a062178_list = scanl (+) 0 a002083_list
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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