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A147537
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Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n digits 0.
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8
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2, 28, 248, 2032, 16352, 131008, 1048448, 8388352, 67108352, 536869888, 4294965248, 34359734272, 274877898752, 2199023239168, 17592186011648, 140737488289792, 1125899906711552, 9007199254478848, 72057594037403648, 576460752302374912, 4611686018425290752
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OFFSET
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1,1
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COMMENTS
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a(n) is the number whose binary representation is A138118(n).
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LINKS
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FORMULA
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a(n) = 2^(n-1)*(4^n - 2) = 2*A147590(n).
a(n) = 10*a(n-1) - 16*a(n-2).
G.f.: 2*x*(1+4*x)/((1-2*x)*(1-8*x)). (End)
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MAPLE
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MATHEMATICA
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Table[FromDigits[Join[Table[1, {2n - 1}], Table[0, {n}]], 2], {n, 1, 20}] (* Stefan Steinerberger, Nov 11 2008 *)
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PROG
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(PARI) vector(20, n, 2^n*(2^(2*n-1)-1)) \\ G. C. Greubel, Jan 12 2020
(Magma) [2^n*(2^(2*n-1)-1): n in [1..20]] // G. C. Greubel, Jan 12 2020
(Sage) [2^n*(2^(2*n-1)-1) for n in (1..20)] # G. C. Greubel, Jan 12 2020
(GAP) List([1..20], n-> 2^n*(2^(2*n-1)-1)); # G. C. Greubel, Jan 12 2020
(Python)
def a(n): return ((1 << (2*n-1)) - 1) << n
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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