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A073941
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a(n) = ceiling(sum{a(k): 1<=k<n} / 2); a(1)=1.
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89
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1, 1, 1, 2, 3, 4, 6, 9, 14, 21, 31, 47, 70, 105, 158, 237, 355, 533, 799, 1199, 1798, 2697, 4046, 6069, 9103, 13655, 20482, 30723, 46085, 69127, 103691, 155536, 233304, 349956, 524934, 787401, 1181102, 1771653, 2657479, 3986219, 5979328, 8968992
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..500
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FORMULA
| a(n) = ceiling(c*(3/2)^n-1/2) where c = 0.3605045561966149591015446628665... - Benoit Cloitre, Nov 22, 2002
If 2^m divides a(i) then 2^(m-1)*3^1 divides a(i+1) and so on... until finally, 3^m divides a(i+m). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 20 2003
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MATHEMATICA
| f[s_] := Append[s, Ceiling[Plus @@ s/2]]; Nest[f, {1}, 41] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 07 2006)
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PROG
| (PARI) v=vector(100); s=v[1]=1; for(i=2, #v, s+=(v[i]=(s+1)\2)); v \\ Charles R Greathouse IV, Feb 11 201
(Haskell)
a073941 n = a073941_list !! (n-1)
a073941_list = 1 : f [1] where
f xs = x' : f (x':xs) where x' = (1 + sum xs) `div` 2
-- Reinhard Zumkeller, Oct 26 2011
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CROSSREFS
| Same as log2(A082125(n)), for n>2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 16 2002
Apart from initial term, same as A005428, which has further information.
a(n+4) = A079719(n)+2. Cf. A082416.
Partial sums for various start indices are in A006999, A061419, A061418. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 17 2003
Is this the same as A081848/3?
The constant c is 2/9*K(3) (see A083286). - Ralf Stephan, May 29, 2003
Sequence in context: A022859 A039884 A078620 * A005428 A143951 A058355
Adjacent sequences: A073938 A073939 A073940 * A073942 A073943 A073944
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KEYWORD
| nonn,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 20 2002
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