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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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15
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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
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OFFSET
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1,1
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COMMENTS
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a(n) is also the number of induced subgraphs with odd number of edges in the path graph P(n) if n>0. - Alessandro Cosentino (cosenal(AT)gmail.com), Feb 06 2009
Also, the decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 566", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 05 2017
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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LINKS
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FORMULA
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"BHK" (reversible, identity, unlabeled) transform of 2, 0, 0, 0, ...
G.f.: 2*x+x^2/((1-2*x)*(1-2*x^2)). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004
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MATHEMATICA
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PROG
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(Magma) [2] cat [2^(n-1)-2^Floor((n-1)/2) : n in [2..40]]; // Wesley Ivan Hurt, Jul 03 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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