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

5, 1, 13, 5, 29, 5, 53, 17, 85, 13, 125, 37, 173, 25, 229, 65, 293, 41, 365, 101, 445, 61, 533, 145, 629, 85, 733, 197, 845, 113, 965, 257, 1093, 145, 1229, 325, 1373, 181, 1525, 401, 1685, 221, 1853, 485, 2029, 265, 2213, 577, 2405, 313, 2605, 677, 2813, 365, 3029

Offset: 1

Author

Kival Ngaokrajang, Jun 13 2014

Keywords

• nonn
• frac
• easy

Comments

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.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Kival Ngaokrajang, Illustration for n = 1..5
• Wikipedia, Sagitta

Crossrefs

Cf. A143025, A001844, A001971.

Programs

PARI

a(n) = numerator(n^2/8+1/2);

Formula

a(n) = numerator(n^2/8 + 1/2).

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