OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = binomial(n^2,3) = 1/6*n^2*(n^2-1)*(n^2-2). - Martin Renner, May 23 2010
G.f.: 4*x^2*(1+x)*(1+13*x+x^2)/(1-x)^7. - Colin Barker, Jan 19 2012
a(1)=0, a(2)=4, a(3)=84, a(4)=560, a(5)=2300, a(6)=7140, a(7)=18424, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Nov 09 2012
Sum_{n>=2} 1/a(n) = Pi^2/2 - 15/4 - 3*Pi*cot(sqrt(2)*Pi)/(2*sqrt(2)). - Amiram Eldar, Feb 17 2024
MATHEMATICA
Binomial[Range[30]^2, 3] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 4, 84, 560, 2300, 7140, 18424}, 30] (* Harvey P. Dale, Nov 09 2012 *)
PROG
(PARI) a(n)=binomial(n^2, 3) \\ Charles R Greathouse IV, Feb 19 2017
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Martin Renner, May 22 2010
EXTENSIONS
Extended by Ray Chandler, May 03 2011
Corrected by Harvey P. Dale, Nov 09 2012
STATUS
approved