This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A134030 #40 Sep 24 2024 06:16:06 %S A134030 0,1,2,3,4,5,6,8,9,11,13,15,18,20,23,26,28,32,35,38,42,46,49,54,58,62, %T A134030 67,71,76,81,86,92,97,103,109,115,121,127,134,140,147,154,161,168,176, %U A134030 183,191,199,207,215,223,232,240,249,258,267,277,286 %N A134030 Area of regular n-sided polygon with length of each side equal to 1 (rounded). %H A134030 Felix Huber, <a href="/A134030/b134030.txt">Table of n, a(n) for n = 3..10000</a> %H A134030 Kival Ngaokrajang, <a href="/A134030/a134030.pdf">Illustration of initial terms</a>. %H A134030 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a>. %F A134030 a(n) = round(n/(4*tan(Pi/n))). %e A134030 The exact values of the areas of regular n-gons with side 1 for n = 3 .. 12 are: %e A134030 (1/4)*3^(1/2), 1, (5/4)*cot((1/5)*Pi), (3/2)*3^(1/2), (7/4)*cot((1/7)*Pi), 2*cot((1/8)*Pi), (9/4)*cot((1/9)*Pi), (5/2)*cot((1/10)*Pi), (11/4)*cot((1/11)*Pi), 3*cot((1/12)*Pi). %e A134030 The floating-point values are [0.4330127020, 1, 1.720477400, 2.598076212, 3.633912443, 4.828427124, 6.181824193, 7.694208842, 9.365639904, 11.19615242], so the rounded values are [0, 1, 2, 3, 4, 5, 6, 8, 9, 11]. - _N. J. A. Sloane_, Mar 11 2024 %o A134030 (PARI) a(n) = round(n / (4*tan(Pi/n))); \\ _Michel Marcus_, Sep 04 2013 %Y A134030 Cf. A064313 (same with floor). %K A134030 easy,nonn %O A134030 3,3 %A A134030 _Ben Paul Thurston_, Jan 11 2008 %E A134030 Corrected by _N. J. A. Sloane_, Mar 11 2024 at the suggestion of _Felix Huber_