login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181286 Partial sums of floor(n^2/3) (A000212). 1
0, 0, 1, 4, 9, 17, 29, 45, 66, 93, 126, 166, 214, 270, 335, 410, 495, 591, 699, 819, 952, 1099, 1260, 1436, 1628, 1836, 2061, 2304, 2565, 2845, 3145, 3465, 3806, 4169, 4554, 4962, 5394, 5850, 6331, 6838, 7371, 7931, 8519, 9135, 9780, 10455, 11160, 11896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Column sums of:

1 4 9 16 25 36 49...

       1  4  9 16...

                1...

....................

--------------------

1 4 9 17 29 45 66...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = Sum_{k=0..n} floor(k^2/3).

a(n) = round((2*n^3 + 3*n^2 - 3*n)/18).

a(n) = round((2*n^3 + 3*n^2 - 3*n - 2)/18).

a(n) = floor((2*n^3 + 3*n^2 - 3*n)/18).

a(n) = ceiling((2*n^3 + 3*n^2 - 3*n - 4)/18).

a(n) = a(n-3) + (n-1)^2, n > 2.

G.f.: x^2*(1+x)/((1-x)^3*(1-x^3)).

G.f.: x^2*(1+x)/((1+x+x^2)*(1-x)^4). - L. Edson Jeffery, Jan 16 2014

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6), n >= 6. - L. Edson Jeffery, Jan 16 2014

EXAMPLE

a(5) = 17 = 0 + 0 + 1 + 3 + 5 + 8.

MAPLE

a(n):=round((2*n^(3)+3*n^(2)-3*n)/(18))

MATHEMATICA

Accumulate[Floor[Range[0, 80]^2/3]] (* Harvey P. Dale, Jun 14 2015 *)

PROG

(MAGMA) [Round((2*n^(3)+3*n^(2)-3*n)/(18)): n in [0..50]]; // Vincenzo Librandi, Jun 21 2011

CROSSREFS

Cf. A000212.

Sequence in context: A008110 A008224 A036594 * A008138 A301123 A265047

Adjacent sequences:  A181283 A181284 A181285 * A181287 A181288 A181289

KEYWORD

nonn

AUTHOR

Mircea Merca, Oct 12 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)