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A178742
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Partial sums of floor(2^n/9).
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2
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0, 0, 0, 0, 1, 4, 11, 25, 53, 109, 222, 449, 904, 1814, 3634, 7274, 14555, 29118, 58245, 116499, 233007, 466023, 932056, 1864123, 3728258, 7456528, 14913068, 29826148, 59652309, 119304632, 238609279, 477218573, 954437161
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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a(n) = round((8*2^n - 18*n - 9)/36).
a(n) = floor((4*2^n - 9*n + 2)/18).
a(n) = ceiling((4*2^n - 9*n - 11)/18).
a(n) = round((4*2^n - 9*n - 4)/18).
a(n) = a(n-6) + 7*2^(n-5) - 3, n > 5.
a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 4*a(n-4) - 5*a(n-5) + 2*a(n-6).
G.f.: x^4 / ( (1-2*x)*(1+x)*(1-x+x^2)*(1-x)^2 ).
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EXAMPLE
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a(6) = 0 + 0 + 0 + 0 + 1 + 3 + 7 = 11.
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MAPLE
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A178742 := proc(n) add( floor(2^i/9), i=0..n) ; end proc:
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MATHEMATICA
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CoefficientList[Series[x^4/((1-2x)(1+x)(1-x+x^2)(1-x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
LinearRecurrence[{4, -5, 1, 4, -5, 2}, {0, 0, 0, 0, 1, 4}, 40] (* Harvey P. Dale, Jan 25 2015 *)
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PROG
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(Magma) [&+[Floor(2^k/9): k in [0..n]]: n in [0..25]]; // Bruno Berselli, Apr 26 2011
(Magma) I:=[0, 0, 0, 0, 1, 4]; [n le 6 select I[n] else 4*Self(n-1)-5*Self(n-2)+Self(n-3)+4*Self(n-4)-5*Self(n-5)+2*Self(n-6): n in [1..40]]; // Vincenzo Librandi, Mar 26 2014
(PARI) vector(30, n, n--; ((4*2^n-9*n+2)/18)\1) \\ G. C. Greubel, Jan 24 2019
(Sage) [floor((4*2^n-9*n+2)/18) for n in (0..30)] # G. C. Greubel, Jan 24 2019
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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STATUS
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approved
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