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A092431
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Numbers having in binary representation a leading 1 followed by n zeros and n-1 ones.
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3
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2, 9, 35, 135, 527, 2079, 8255, 32895, 131327, 524799, 2098175, 8390655, 33558527, 134225919, 536887295, 2147516415, 8590000127, 34359869439, 137439215615, 549756338175, 2199024304127, 8796095119359
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n+1) = 2*a(n) + 4^n + 1;
Smallest numbers having in binary representation n 0's and n 1's:
a(n) = Min{m: A023416(m)=A000120(m)=n};
subsequence of A031443.
a(n) = A007582(n)-1 = A056326(2n+1) = A005367(n-1)/2 = A063376(n)/2-1 = A032125(n+1)/3-1 = A056309(2n+1)/2 = A028403(n+1)/4-1 = (A001576(n)-3)/2 = (A028400(n+1)-9)/8 = sum(k=2,n+1, A049775(k)) - R. Stephan, Mar 24 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Binary
Index to sequences with linear recurrences with constant coefficients, signature (7,-14,8).
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FORMULA
| a(n) = 2^(2*n-1) + 2^(n-1) - 1.
G.f. x*(-2+5*x) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Jun 01 2011
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CROSSREFS
| Cf. A007088, A001700.
Sequence in context: A032601 A083141 A001571 * A147762 A077837 A150945
Adjacent sequences: A092428 A092429 A092430 * A092432 A092433 A092434
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 23 2004
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