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A055010
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a(0) = 0; for n > 0, a(n) = 3*2^(n-1) - 1.
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41
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0, 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, 805306367, 1610612735, 3221225471, 6442450943, 12884901887
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OFFSET
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0,2
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COMMENTS
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Apart from leading term (which should really be 3/2), same as A083329.
Written in binary, a(n) is 1011111...1.
The sequence 2, 5, 11, 23, 47, 95, ... apparently gives values of n such that Nim-factorial(n) = 2. Cf. A059970. However, compare A060152. More work is needed! - John W. Layman, Mar 09 2001
With offset 1, number of (132,3412)-avoiding two-stack sortable permutations.
Number of descents after n+1 iterations of morphism A007413.
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=[i,i]:=1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^n*charpoly(A,-1). - Milan Janjic, Jan 24 2010
a(n) is the total number of records over all length n binary words. A record in a word a_1,a_2,...,a_n is a letter a_j that is larger than all the preceding letters. That is, a_j>a_i for all i<j. - Geoffrey Critzer, Jul 18 2020
Called Thabit numbers after the Syrian mathematician Thābit ibn Qurra (826 or 836 - 901). - Amiram Eldar, Jun 08 2021
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 3*2^2 - 1 = 3*4 - 1 = 11.
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MATHEMATICA
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PROG
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(Sage) [0]+[3*2^(n-1)-1 for n in (1..35)] # G. C. Greubel, May 06 2019
(GAP) Concatenation([0], List([1..35], n-> 3*2^(n-1)-1)) # G. C. Greubel, May 06 2019
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CROSSREFS
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Cf. A266550 (independence number of the n-Mycielski graph).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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