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 A338422 Place four points evenly spaced on a circle, draw n evenly spaced rays from each of the points, a(n) is the number of vertices thus created. See Comments for details. 3
 4, 5, 24, 21, 64, 45, 96, 37, 152, 129, 216, 173, 304, 261, 384, 185, 488, 441, 600, 517, 736, 669, 864, 453, 1016, 945, 1176, 1053, 1360, 1269, 1536, 1025, 1736, 1641, 1944, 1781, 2176, 2061, 2400, 1717, 2648, 2529, 2904, 2701, 3184, 3045, 3456, 2465, 3752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The rays are evenly spaced around each point. The first ray from each point goes opposite to the direction to the center of the circle. Should a ray hit another point it is terminated there. See A338421 for illustrations. LINKS Lars Blomberg, Table of n, a(n) for n = 1..642 FORMULA Conjectured for 3 <= n <= 642. Select the row in the table below for which r = n mod m. Then a(n)=(a*n^2 + b*n + c)/d. +==================================+ |      r |  m | a |   b |    c | d | +----------------------------------+ |      2 |  4 | 3 |  -6 |   18 | 2 | |      3 |  4 | 3 |   6 |    3 | 2 | |      1 |  8 | 3 |   6 |    7 | 2 | |      4 |  8 | 3 | -10 |   34 | 2 | |      5 |  8 | 3 |   6 |   23 | 2 | |      0 | 48 | 3 | -39 | -110 | 2 | |  8, 40 | 48 | 3 | -39 |  194 | 2 | | 16, 32 | 48 | 3 | -39 |  226 | 2 | |     24 | 48 | 3 | -39 |  114 | 2 | +==================================+ EXAMPLE For n=1 there are four rays that do not intersect, so a(1)=4. PROG (PARI) a(n)={ if( n==1, 4, n==2, 5, n%4==2, (3*n^2 - 6*n + 18)/2, n%4==3, (3*n^2 + 6*n + 3)/2, n%8==1, (3*n^2 + 6*n + 7)/2, n%8==4, (3*n^2 - 10*n + 34)/2, n%8==5, (3*n^2 + 6*n + 23)/2, n%48==0, (3*n^2 - 39*n - 110)/2, n%48==8||n%48==40, (3*n^2 - 39*n + 194)/2, n%48==16||n%48==32, (3*n^2 - 39*n + 226)/2, n%48==24, (3*n^2 - 39*n + 114)/2, -1); } vector(642, n, a(n)) CROSSREFS Cf. A338123, A338421 (regions), A338423 (edges). Sequence in context: A176957 A341586 A010302 * A171885 A331261 A063986 Adjacent sequences:  A338419 A338420 A338421 * A338423 A338424 A338425 KEYWORD nonn AUTHOR Lars Blomberg, Oct 26 2020 STATUS approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)