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 A062178 a(n+1) = 2a(n)-a([n/2]) starting with a(0)=0 and a(1)=1. 4
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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] For n > 0: a(n) = A005255(n-1) + 1. - Reinhard Zumkeller, Nov 18 2012 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 FORMULA a(n) =a(n-1)+A002083(n). EXAMPLE 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. PROG (Haskell) a062178 n = a062178_list !! (n-1) a062178_list = scanl (+) 0 a002083_list -- Reinhard Zumkeller, Nov 18 2012 CROSSREFS Sequence in context: A125028 A119262 A177510 * A173282 A178833 A212657 Adjacent sequences:  A062175 A062176 A062177 * A062179 A062180 A062181 KEYWORD nonn AUTHOR Henry Bottomley, Jun 12 2001 STATUS approved

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)