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A174709
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Partial sums of floor(n/6).
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11
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0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 85, 90, 96, 102, 108, 114, 120, 126, 133, 140, 147, 154, 161, 168, 176, 184, 192
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OFFSET
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0,8
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COMMENTS
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Partial sums of A152467.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,1)
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
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FORMULA
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a(n) = round(n*(n-4)/12) = round((2*n^2-8*n-1)/24).
a(n) = floor((n-2)^2/12).
a(n) = ceil((n+1)*(n-5)/12).
a(n) = a(n-6)+n-5, n>5.
Contribution from R. J. Mathar, Nov 30 2010: (Start)
a(n)= +2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8).
G.f.: -x^6 / ( (1+x)*(x^2-x+1)*(1+x+x^2)*(x-1)^3 ).
a(n) = -n/3+5/72+n^2/12+(-1)^n/24 + A057079(n+5)/6+A061347(n)/18. (End)
a(6n) = A000567(n), a(6n+1) = 2*A000326(n), a(6n+2) = A033428(n), a(6n+3) = A049451(n), a(6n+4) = A045944(n), a(6n+5) = A028896(n). - Philippe Deléham, Mar 26 2013
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EXAMPLE
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a(7) = floor(0/6)+floor(1/6)+floor(2/6)+floor(3/6)+floor(4/6)+floor(5/6)+floor(6/6)+floor(7,6) = 2
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MAPLE
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a(n):=round(n*(n-4)/12)
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PROG
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(MAGMA) [Round(n*(n-4)/12): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011
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CROSSREFS
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Cf. A152467.
Sequence in context: A004279 A120370 A011866 * A008724 A112402 A056864
Adjacent sequences: A174706 A174707 A174708 * A174710 A174711 A174712
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KEYWORD
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nonn,easy
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AUTHOR
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Mircea Merca, Nov 30 2010
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STATUS
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approved
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