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A243883 Numerator of circle radius r(n) at constant unit length sagitta and chord length = n.

%I A243883 #28 Aug 04 2025 11:38:01
%S A243883 5,1,13,5,29,5,53,17,85,13,125,37,173,25,229,65,293,41,365,101,445,61,
%T A243883 533,145,629,85,733,197,845,113,965,257,1093,145,1229,325,1373,181,
%U A243883 1525,401,1685,221,1853,485,2029,265,2213,577,2405,313,2605,677,2813,365,3029
%N A243883 Numerator of circle radius r(n) at constant unit length sagitta and chord length = n.
%C A243883 Denominator of circle radius r(n) is A143025(n+2). The integral radius appearing at n = 2, 6, 10, 14, ..., = 1, 5, 13, 25, ..., respectively which is A001844(n/4 - 1/2). Floor (r(n)) = A001971(n). For the case of sagitta = n and chord length = 1, the numerator and the denominator will be A053755(n) and A008590(n) respectively. See illustration in links.
%H A243883 Colin Barker, <a href="/A243883/b243883.txt">Table of n, a(n) for n = 1..1000</a>
%H A243883 Kival Ngaokrajang, <a href="/A243883/a243883.pdf">Illustration for n = 1..5</a>
%H A243883 Wikipedia, <a href="http://en.wikipedia.org/wiki/Circle">Sagitta</a>
%F A243883 a(n) = numerator(n^2/8 + 1/2).
%F A243883 Empirical g.f.: -x*(x^11 +5*x^10 +x^9 +13*x^8 +2*x^7 +14*x^6 +2*x^5 +14*x^4 +5*x^3 +13*x^2 +x +5) / ((x -1)^3*(x +1)^3*(x^2 +1)^3). - _Colin Barker_, Jan 17 2015
%o A243883 (PARI) a(n) = numerator(n^2/8+1/2);
%Y A243883 Cf. A143025, A001844, A001971.
%K A243883 nonn,frac,easy
%O A243883 1,1
%A A243883 _Kival Ngaokrajang_, Jun 13 2014