Search: id:A033156
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%I A033156
%S A033156 1,4,8,12,17,22,27,32,38,44,50,56,62,68,74,80,87,94,101,108,115,122,129,
%T A033156 136,143,150,157,164,171,178,185,192,200,208,216,224,232,240,248,256,264,
%U A033156 272,280,288,296,304,312,320,328,336,344,352,360,368,376,384,392,400,408
%N A033156 a(1) = 1; for m >= 2, a(n) = a(n-1)+floor(a(n-1)/(n-1))+2.
%D A033156 M. A. Nyblom, Some curious sequences ..., Am. Math. Monthly 109 (#6, 
               200), 559-564, Th. 3.1.
%H A033156 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A033156 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A033156 a(n) = n*(floor(log_2 n) + 3) - 2^((floor (log_2 n)) + 1).
%F A033156 a(n) = n+a(floor[n/2])+a(ceiling[n/2]) = n+min{a(k)+a(n-k):0<k<n} = n+A003314(n). 
               - Henry Bottomley (se16(AT)btinternet.com), Jul 03 2002
%F A033156 A001855(n) + 2n-1. a(n) = b(n)+1 with b(0)=0, b(2n) = b(n)+b(n-1)+2n+2, 
               b(2n+1) = 2b(n)+2n+3. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Oct 24 2003
%p A033156 A033156 := proc(n) option remember; if n=1 then 1 else A033156(n-1)+floor(A033156(n-1)/
               (n-1))+2; fi; end;
%Y A033156 Sequence in context: A001956 A106633 A002004 this_sequence A036573 A098573 
               A092753
%Y A033156 Adjacent sequences: A033153 A033154 A033155 this_sequence A033157 A033158 
               A033159
%K A033156 nonn
%O A033156 1,2
%A A033156 N. J. A. Sloane (njas(AT)research.att.com), Jun 05 2002

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