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A164203
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Number of binary strings of length n with equal numbers of 00001 and 10000 substrings.
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1
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1, 2, 4, 8, 16, 30, 58, 114, 226, 452, 904, 1808, 3616, 7232, 14464, 28928, 57856, 115712, 231424, 462848, 925696, 1851392, 3702784, 7405568, 14811136, 29622272, 59244544, 118489088, 236978176, 473956352, 947912704, 1895825408, 3791650816, 7583301632
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 113*2^(n-7) for n >= 8. - Brad Clardy, Feb 11 2012
G.f.: (2*x^8+2*x^7+2*x^6+2*x^5-1)/(2*x-1). - Alois P. Heinz, Aug 17 2019
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MATHEMATICA
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CoefficientList[Series[(2x^8+2x^7+2x^6+2x^5-1)/(2x-1), {x, 0, 50}], x] (* or *) LinearRecurrence[{2}, {1, 2, 4, 8, 16, 30, 58, 114, 226}, 50] (* Harvey P. Dale, Apr 23 2022 *)
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PROG
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(Empirical) (bc) (z is number of 0's) z=4; for(i=0; i<=500; i++) { if(i<=z)a=2^i else if(i<=2*z)a=2*a-2 else a=2*a; a }
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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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