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A089207 a(n) = 4n^3 + 2n^2. 0

%I

%S 6,40,126,288,550,936,1470,2176,3078,4200,5566,7200,9126,11368,13950,

%T 16896,20230,23976,28158,32800,37926,43560,49726,56448,63750,71656,

%U 80190,89376,99238,109800,121086,133120,145926,159528,173950,189216

%N a(n) = 4n^3 + 2n^2.

%C 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.

%C 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

%F 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]

%F a(n) = 2 * n * A014105(n). - _Richard R. Forberg_, Jun 16 2013

%Y Cf. A085409, A087887.

%K nonn,easy

%O 1,1

%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 09 2003

%E More terms from _Ray Chandler_, Feb 15 2004

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Last modified April 6 08:53 EDT 2020. Contains 333268 sequences. (Running on oeis4.)