|
| |
|
|
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 (amarnath_murthy(AT)yahoo.com), Jun 20 2002
|
|
|
EXTENSIONS
|
Edited by Robert G. Wilson v, Jun 21 2002
|
|
|
STATUS
|
approved
|
| |
|
|
