A062178 a(n+1) = 2a(n)-a([n/2]) starting with a(0)=0 and a(1)=1.

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

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: A349777 A119262 A177510 * A173282 A178833 A212657

Adjacent sequences: A062175 A062176 A062177 * A062179 A062180 A062181

Keyword

nonn

Author

Henry Bottomley, Jun 12 2001

Status

approved