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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 Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1. Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,-2,1). 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 Cf. A001106, A022264, A022265, A024966, A179986, A186029, A218471. Cf. Similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A118729, A218470, A131242. Sequence in context: A292621 A280693 A281613 * A011867 A008725 A275673 Adjacent sequences: A174735 A174736 A174737 * A174739 A174740 A174741 KEYWORD nonn,easy AUTHOR Mircea Merca, Nov 30 2010 STATUS approved

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