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Search: id:A055010
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| A055010 |
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a(0) = 0; for n > 0, 3*2^(n-1) - 1. |
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+0
19
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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 (layman(AT)math.vt.edu), 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.
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LINKS
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Eric Weisstein's World of Mathematics, Thabit ibn Kurrah Number
E. S. Egge and T. Mansour, 132-avoiding two-stack sortable permutations....
S. Kitaev and T. Mansour, Counting the occurrences of generalized patterns....
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FORMULA
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a(n) = 2*a(n-1) + 1 = a(n-1) + A007283(n-1) = A007283(n)-1 = A000079(n) + A000225(n + 1) = A000079(n + 1) + A000225(n) = 3*A000079(n)-1 = 3*A000225(n) + 2
a(n) = A010036(n)/2^(n-1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 2004
a(n) = A099258(A033484(n)-1) = floor(A033484(n)/2). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 09 2004
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EXAMPLE
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a(3) = 3*2^2-1 = 3*4-1 = 11
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MAPLE
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seq(floor((2^i+2^(i+1)-2)/2), i=0..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007
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CROSSREFS
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Cf. A007505 for primes in this sequence. Apart from initial term, same as A052940 and A083329.
a(n) = A118654(n-1, 4), for n > 0.
Sequence in context: A133489 A060153 A086219 this_sequence A083329 A081973 A055496
Adjacent sequences: A055007 A055008 A055009 this_sequence A055011 A055012 A055013
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 31 2000
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