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Search: id:A141447
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| A141447 |
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Number of n-bead black-white reversible strings; also binary grids; string is not palindromic. |
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+0
5
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| 0, 1, 2, 6, 12, 28, 56, 120, 240, 496, 992, 2016, 4032, 8128, 16256, 32640, 65280, 130816, 261632, 523776, 1047552, 2096128, 4192256, 8386560, 16773120
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=A005418(n+1)-A016116(n+2) analogue of A006516(n)=A007582(n)-A000079(n)
a(n) is also the number of induced subgraphs with odd number of edges in the path graph P(n), with a(1)=0, a(2)=1,... [From Alessandro Cosentino (cosenal(AT)gmail.com), Feb 06 2009]
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FORMULA
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2^(n-1) - 2^[(n-1)/2] a(n+4)=6a(n+2)-8a(n), n=1,2,3,... a(1)=0, a(2)=1, a(3)=2, a(4)=6
a(n)=A122746(n-1), n>0. O.g.f.: x/((1-2x)(1-2x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 27 2008]
a(n+1) = A077957(n) + 2*a(n) with a(1)=0. a(n+2) = A000079(n+1) + 2*a(n) with a(1)=0 a(2)=1. - Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 10 2008
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EXAMPLE
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a(11)=2^(11-1) - 2^[(11-1)/2] = 2^10 - 2^5 = 1024-32 =992
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CROSSREFS
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Cf. A005418, A016116.
Sequence in context: A112510 A011949 A089820 this_sequence A122746 A057582 A094779
Adjacent sequences: A141444 A141445 A141446 this_sequence A141448 A141449 A141450
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KEYWORD
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nonn
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AUTHOR
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Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Aug 07 2008
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