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A174709 Partial sums of floor(n/6). 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Partial sums of A152467.

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,-1,0,0,0,1,-2,1)

FORMULA

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.

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

a(n) = A008724(n-2). - R. J. Mathar, Jul 10 2015

EXAMPLE

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

MAPLE

a(n):=round(n*(n-4)/12)

MATHEMATICA

Table[Sum[Floor[k/9], {k, 0, n}], {n, 0, 25}] (* G. C. Greubel, Dec 13 2016 *)

PROG

(MAGMA) [Round(n*(n-4)/12): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011

(PARI) a(n)=(n-2)^2\12 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A152467.

Sequence in context: A120370 A011866 A292983 * A008724 A287642 A237118

Adjacent sequences:  A174706 A174707 A174708 * A174710 A174711 A174712

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Nov 30 2010

STATUS

approved

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Last modified October 21 20:51 EDT 2018. Contains 316428 sequences. (Running on oeis4.)