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A174738 Partial sums of floor(n/7). 17
0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 24, 27, 30, 33, 36, 39, 42, 46, 50, 54, 58, 62, 66, 70, 75, 80, 85, 90, 95, 100, 105, 111, 117, 123, 129, 135, 141, 147, 154, 161, 168, 175, 182, 189, 196, 204, 212, 220, 228, 236 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Apart from the initial zeros, the same as A011867.
LINKS
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
FORMULA
a(n) = round(n*(n-5)/14).
a(n) = floor((n-2)*(n-3)/14).
a(n) = ceiling((n+1)*(n-6)/14).
a(n) = a(n-7) + n - 6, n > 6.
a(n) = +2*a(n-1) - a(n-2) + a(n-7) - 2*a(n-8) + a(n-9). - R. J. Mathar, Nov 30 2010
G.f.: x^7/( (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1-x)^3 ). - R. J. Mathar, Nov 30 2010
a(7n) = A001106(n), a(7n+1) = A218471(n), a(7n+2) = A022264(n), a(7n+3) = A022265(n), a(7n+4) = A186029(n), a(7n+5) = A179986(n), a(7n+6) = A024966(n). - Philippe Deléham, Mar 26 2013
EXAMPLE
a(9) = floor(0/7) + floor(1/7) + floor(2/7) + floor(3/7) + floor(4/7) + floor(5/7) + floor(6/7) + floor(7/7) + floor(8/7) + floor(9/7) = 3.
MAPLE
A174738 := proc(n) round(n*(n-5)/14) ; end proc:
seq(A174738(n), n=0..30) ;
MATHEMATICA
Table[Floor[(n - 2)*(n - 3)/14], {n, 0, 60}] (* G. C. Greubel, Dec 13 2016 *)
PROG
(Magma) [Round(n*(n-5)/14): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011
(PARI) a(n)=(n-2)*(n-3)\14 \\ Charles R Greathouse IV, Sep 24 2015
(Sage) [floor((n-2)*(n-3)/14) for n in (0..60)] # G. C. Greubel, Aug 31 2019
(GAP) List([0..60], n-> Int((n-2)*(n-3)/14)); # G. C. Greubel, Aug 31 2019
CROSSREFS
Sequence in context: A292621 A280693 A281613 * A011867 A008725 A275673
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Nov 30 2010
STATUS
approved

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