%I #17 Jun 13 2015 00:50:16

%S 4,3,12,8,24,15,40,24,60,35,84,48,112,63,144,80,180,99,220,120,264,

%T 143,312,168,364,195,420,224,480,255,544,288,612,323,684,360,760,399,

%U 840,440,924,483,1012,528,1104,575,1200,624,1300,675,1404,728,1512,783

%N Longest other leg of a Pythagorean triangle with n as length of a leg.

%H Todd Silvestri, <a href="/A055523/b055523.txt">Table of n, a(n) for n = 3..1002</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).

%F a(n) = 2*A055522(n)/n = sqrt(A055524(n)^2-n^2).

%F a(2k) = (k-1)*(k+1), a(2k+1) = 2k*(k+1).

%F a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: x^3*(x^3-3*x-4) / ((x-1)^3*(x+1)^3). - _Colin Barker_, Sep 15 2014

%F a(n) = (3*(n^2-2)+(-1)^(n+1)*(n^2+2))/8. - _Todd Silvestri_, Dec 16 2014

%F E.g.f.: 1 + (3*x^2/8 + 3*x/8 - 3/4)*exp(x) + (-x^2/8 + x/8 - 1/4)*exp(-x). - _Robert Israel_, Dec 16 2014

%p seq(`if`(n::even, (n/2-1)*(n/2+1), (n-1)*(n+1)/2), n=3..100); # _Robert Israel_, Dec 16 2014

%t a[n_Integer/;n>=3]:=(3 (n^2-2)+(-1)^(n+1) (n^2+2))/8 (* _Todd Silvestri_, Dec 16 2014 *)

%o (PARI) Vec(x^3*(x^3-3*x-4)/((x-1)^3*(x+1)^3) + O(x^100)) \\ _Colin Barker_, Sep 15 2014

%Y Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055524, A055525, A055526, A055527.

%K nonn,easy

%O 3,1

%A _Henry Bottomley_, May 22 2000