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A174738 Partial sums of floor(n/7). 16
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

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,-2,1).

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

FORMULA

a(n) = round(n*(n-5)/14).

a(n) = floor((n-2)*(n-3)/14).

a(n) = ceil((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 / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^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, 50}] (* 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

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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Last modified October 20 04:37 EDT 2018. Contains 316378 sequences. (Running on oeis4.)