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!)
A171965 Partial sums of floor(n^2/6) (A056827). 2
0, 0, 0, 1, 3, 7, 13, 21, 31, 44, 60, 80, 104, 132, 164, 201, 243, 291, 345, 405, 471, 544, 624, 712, 808, 912, 1024, 1145, 1275, 1415, 1565, 1725, 1895, 2076, 2268, 2472, 2688, 2916, 3156, 3409, 3675, 3955, 4249, 4557, 4879, 5216, 5568, 5936, 6320, 6720, 7136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Quasipolynomial.

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 (3,-3,1,0,0,1,-3,3,-1).

FORMULA

a(n) = Sum_{k=0..n} floor(k^2/6)).

a(n) = round((2*n^3 + 3*n^2 - 12*n - 6)/36).

a(n) = round((4*n^3 + 6*n^2 - 24*n - 13)/72).

a(n) = floor((2*n^3 + 3*n^2 - 12*n + 7)/36).

a(n) = ceiling((2*n^3 + 3*n^2 - 12*n - 20)/36).

a(n) = a(n-6) + n^2 - 5*n + 7, n > 5.

G.f.: x^3*(1+x^2) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^4 ). - R. J. Mathar, Jan 28 2012

EXAMPLE

a(5) = 7 = 0 + 0 + 0 + 1 + 2 + 4.

MAPLE

a(n):=round((2*n^3 +3*n^2 -12*n-6)/36)

PROG

(MAGMA) [Round((2*n^3+3*n^2-12*n-6)/36): n in [0..60]]; // Vincenzo Librandi, Jun 25 2011

(PARI) a(n)=(2*n^3+3*n^2-12*n+7)\36 \\ Charles R Greathouse IV, Jan 29 2012

CROSSREFS

Cf. A056827.

Sequence in context: A247890 A063541 A206246 * A011898 A098577 A004136

Adjacent sequences:  A171962 A171963 A171964 * A171966 A171967 A171968

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Nov 19 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 February 28 00:28 EST 2020. Contains 332319 sequences. (Running on oeis4.)