login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A177205 Partial sums of round(n^2/17). 1
0, 0, 0, 1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 48, 60, 73, 88, 105, 124, 145, 169, 195, 223, 254, 288, 325, 365, 408, 454, 503, 556, 613, 673, 737, 805, 877, 953, 1034, 1119, 1208, 1302, 1401, 1505, 1614, 1728, 1847, 1971, 2101, 2237, 2378, 2525 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The round function is defined here by round(x)=floor(x+1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..890

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+1)*(2*n+1)/102).

a(n)=floor((2*n^3+3*n^2+n+36)/102).

a(n)=ceil((2*n^3+3*n^2+n-36)/102).

a(n)=a(n-17)+(n+1)*(n-17)+105 , n>16.

a(n)= +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-17) -3*a(n-18) +3*a(n-19) -a(n-20) with g.f. x^3 *(1+x) *(x^12-2*x^11+2*x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+2*x^2-2*x+1) / ( (x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) *(x-1)^4 ). - R. J. Mathar, Dec 13 2010

EXAMPLE

a(17) = 0+0+0+1+1+1+2+3+4+5+6+7+8+10+12+13+15+17 = 105.

MAPLE

seq(round(n*(n+1)*(2*n+1)/102), n=0..50)

PROG

(MAGMA) [Floor((2*n^3+3*n^2+n+36)/102): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

CROSSREFS

Cf. A177100, A177116.

Sequence in context: A104664 A022856 A089071 * A275580 A175829 A241552

Adjacent sequences:  A177202 A177203 A177204 * A177206 A177207 A177208

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Dec 10 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 23 09:52 EST 2017. Contains 295115 sequences.