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A178460
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Partial sums of floor(2^n/127).
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2
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0, 0, 0, 0, 0, 0, 1, 3, 7, 15, 31, 63, 127, 256, 514, 1030, 2062, 4126, 8254, 16510, 33023, 66049, 132101, 264205, 528413, 1056829, 2113661, 4227326, 8454656, 16909316, 33818636, 67637276
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OFFSET
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1,8
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COMMENTS
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LINKS
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FORMULA
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a(n) = round((14*2^n - 127*n + 75)/889).
a(n) = floor((14*2^n - 127*n + 284)/889).
a(n) = ceiling((14*2^n - 127*n - 134)/889).
a(n) = round((14*2^n - 127*n - 14)/889).
a(n) = a(n-7) + 2^(n-6) - 1, n > 6.
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-7) - 3*a(n-8) + 2*a(n-9), n > 9.
G.f.: -x^7/((2*x-1)*(x-1)^2*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)).
a(n) = Sum_{k=0..n} 2^(n-k) * floor(k/7).
a(n) = floor(2^(n+1)/127) - floor((n+1)/7). (End)
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EXAMPLE
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a(10) = a(3) + 2^4 - 1 = 15.
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MAPLE
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A178460 := proc(n) add( floor(2^i/127), i=0..n) ; end proc:
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PROG
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(Magma) [Round((14*2^n-127*n+75)/889): n in [1..40]]; // Vincenzo Librandi, Jun 21 2011
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CROSSREFS
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KEYWORD
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nonn,easy,less,changed
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AUTHOR
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STATUS
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approved
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