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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072474 Sum of next n squares. 11
1, 13, 77, 294, 855, 2071, 4403, 8492, 15189, 25585, 41041, 63218, 94107, 136059, 191815, 264536, 357833, 475797, 623029, 804670, 1026431, 1294623, 1616187, 1998724, 2450525, 2980601, 3598713, 4315402, 5142019, 6090755, 7174671 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..31.

FORMULA

a(n) = k(k+1)(2k+1)/6 - r(r+1)(2r+1)/6, where k = n(n+1)/2 and r = n(n-1)/2.

a(n) = (n/12) *(3n^2+1)*(n^2+2). - Benoit Cloitre, Jun 26 2002

G.f.: x*(1+3*x+x^2)*(1+4*x+x^2)/(1-x)^6. - Colin Barker, Mar 23 2012

EXAMPLE

1^2 = 1; 2^2 + 3^2 = 13; 4^2 + 5^2 + 6^2 = 77; ...

MATHEMATICA

Table[Sum[ i^2, {i, n(n - 1)/2 + 1, n(n + 1)/2}], {n, 1, 35}]

PROG

(PARI) for(n=1, 50, print1(n*(3*n^2+1)*(n^2+2)/12, ", "))

CROSSREFS

Cf. A072475, A050410.

Sequence in context: A044200 A044581 A126423 * A186103 A194713 A047638

Adjacent sequences:  A072471 A072472 A072473 * A072475 A072476 A072477

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Jun 20 2002

EXTENSIONS

Edited by Robert G. Wilson v, Jun 21 2002

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 February 24 22:26 EST 2018. Contains 299627 sequences. (Running on oeis4.)