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Search: id:A033156
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| A033156 |
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a(1) = 1; for m >= 2, a(n) = a(n-1)+floor(a(n-1)/(n-1))+2. |
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+0
2
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| 1, 4, 8, 12, 17, 22, 27, 32, 38, 44, 50, 56, 62, 68, 74, 80, 87, 94, 101, 108, 115, 122, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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M. A. Nyblom, Some curious sequences ..., Am. Math. Monthly 109 (#6, 200), 559-564, Th. 3.1.
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(n) = n*(floor(log_2 n) + 3) - 2^((floor (log_2 n)) + 1).
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
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
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MAPLE
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A033156 := proc(n) option remember; if n=1 then 1 else A033156(n-1)+floor(A033156(n-1)/(n-1))+2; fi; end;
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CROSSREFS
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Sequence in context: A001956 A106633 A002004 this_sequence A036573 A098573 A092753
Adjacent sequences: A033153 A033154 A033155 this_sequence A033157 A033158 A033159
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 05 2002
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