A062178 - OEIS

%I #9 Jul 13 2013 12:02:40

%S 0,1,2,3,5,8,14,25,47,89,173,338,668,1322,2630,5235,10445,20843,41639,

%T 83189,166289,332405,664637,1328936,2657534,5314400,10628132,21254942,

%U 42508562,85014494,170026358,340047481,680089727,1360169009,2720327573

%N a(n+1) = 2a(n)-a([n/2]) starting with a(0)=0 and a(1)=1.

%C 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.

%C The subsequence of primes in this partial sum begins: 2, 3, 5, 47, 89, 173, 166289. [From _Jonathan Vos Post_, Feb 17 2010]

%C For n > 0: a(n) = A005255(n-1) + 1. - _Reinhard Zumkeller_, Nov 18 2012

%H Reinhard Zumkeller, <a href="/A062178/b062178.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) =a(n-1)+A002083(n).

%e 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.

%o (Haskell)

%o a062178 n = a062178_list !! (n-1)

%o a062178_list = scanl (+) 0 a002083_list

%o -- _Reinhard Zumkeller_, Nov 18 2012

%K nonn

%O 0,3

%A _Henry Bottomley_, Jun 12 2001