OFFSET
1,1
COMMENTS
Yet another parametric representation of the solutions of the Diophantine equation x^2 - y^2 = z^3 is (3n^3, n^3, 2n^2). By taking the sum x+y+z we get a(n) = 4n^3 + 2n^2.
If Y is a 3-subset of an 2n-set X then, for n>=5, a(n-2) is the number of 5-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 2*A099721(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: 2*x*(3+8*x+x^2)/(x-1)^4. [R. J. Mathar, Apr 20 2009]
a(n) = 2 * n * A014105(n). - Richard R. Forberg, Jun 16 2013
MATHEMATICA
Table[4n^3+2n^2, {n, 40}] (* Harvey P. Dale, Jun 12 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 09 2003
EXTENSIONS
More terms from Ray Chandler, Feb 15 2004
STATUS
approved