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A032085
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Number of reversible strings with n beads of 2 colors. If more than 1 bead, not palindromic.
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8
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2, 1, 2, 6, 12, 28, 56, 120, 240, 496, 992, 2016, 4032, 8128, 16256, 32640, 65280, 130816, 261632, 523776, 1047552, 2096128, 4192256, 8386560, 16773120, 33550336, 67100672, 134209536, 268419072, 536854528
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) is also the number of induced subgraphs with odd number of edges in the path graph P(n) if n>0. [From Alessandro Cosentino (cosenal(AT)gmail.com), Feb 06 2009]
A common recurrence of the bisections A020522 and A006516 means a(n+4)=6a(n+2)-8a(n), n>1. [Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 07 2008]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
C. G. Bower, Transforms (2)
Index to sequences with linear recurrences with constant coefficients, signature (2,2,-4).
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1022
S. J. Cyvin et al., Theory of polypentagons, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474.
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FORMULA
| "BHK" (reversible, identity, unlabeled) transform of 2, 0, 0, 0...
a(n) = 2^(n-1)-2^floor((n-1)/2), n > 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 11 2001
g.f.: 2*x+x^2/((1-2*x)*(1-2*x^2)) - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004
a(n)=A005418(n+1)-A016116(n+2), n>1. [Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 07 2008]
a(n+1) = A077957(n) + 2*a(n), n>1. a(n+2) = A000079(n+1) + 2*a(n), n>1. - Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 10 2008
First differences: a(n+1)-a(n) = A007179(n) = A156232(n+2)/4, n>1. [Paul Curtz, Nov 16 2009]
a(n)=2*(a(n-1) bitwiseOR a(n-2)), n>3. [Pierre Charland, Dec 12 2010]
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CROSSREFS
| Cf. A005418, A016116. Essentially the same as A122746.
Row sums of triangle A034877.
Sequence in context: A110422 A131804 A170829 * A032163 A038078 A000139
Adjacent sequences: A032082 A032083 A032084 * A032086 A032087 A032088
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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