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%I #20 Feb 29 2024 14:31:53
%S 5,5,13,10,25,17,41,26,61,37,85,50,113,65,145,82,181,101,221,122,265,
%T 145,313,170,365,197,421,226,481,257,545,290,613,325,685,362,761,401,
%U 841,442,925,485,1013,530,1105,577,1201,626,1301,677,1405,730,1513,785
%N Longest other side of a Pythagorean triangle with n as length of one of the three sides (in fact n is a leg and a(n) the hypotenuse).
%H Paolo Xausa, <a href="/A055524/b055524.txt">Table of n, a(n) for n = 3..10000</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) = sqrt(n^2+A055523(n)^2). a(2k) = k^2+1, a(2k+1) = k^2+(k+1)^2.
%F a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: -x^3*(2*x^5+x^4-5*x^3-2*x^2+5*x+5) / ((x-1)^3*(x+1)^3). - _Colin Barker_, Sep 15 2014
%F a(n) = (3*n^2+6-(n^2-2)*(-1)^n)/8. - _Luce ETIENNE_, Jul 11 2015
%t A055524[n_] := (3*n^2-(-1)^n*(n^2-2)+6)/8; Array[A055524, 100, 3] (* or *)
%t LinearRecurrence[{0, 3, 0, -3, 0, 1}, {5, 5, 13, 10, 25, 17}, 100] (* _Paolo Xausa_, Feb 29 2024 *)
%o (PARI) Vec(-x^3*(2*x^5+x^4-5*x^3-2*x^2+5*x+5)/((x-1)^3*(x+1)^3) + O(x^100)) \\ _Colin Barker_, Sep 15 2014
%Y Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055523, A055525, A055526, A055527.
%K nonn,easy
%O 3,1
%A _Henry Bottomley_, May 22 2000
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