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 A291718 Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1 <= k <= m positions can be picked in an m X m square grid such that the picked positions have a line symmetry. 9
 1, 4, 6, 8, 36, 44, 16, 120, 192, 276, 25, 300, 596, 1130, 2010, 36, 630, 1436, 3321, 6880, 16400, 49, 1176, 3024, 8272, 20600, 57564, 120940, 64, 2016, 5568, 17528, 49184, 159784, 380344, 1075344 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..36. EXAMPLE A configuration of 6 picked points from a 7 X 7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, and no point symmetry would be: o o o o o o o + X o X o o o X + o o o X o o o + o o o o X o o + o o o o o o o + o o o X o o o + o So it would not contribute to the count of central symmetric configurations in A291717(27). . A configuration o o + o o o o o o + o o o o X o + o X o o + X # X + + + X o + o X o o o o + o o o o o o + o o o o would contribute both to a(27) and to A291717(27), because besides being mirror symmetric w.r.t. the lines indicated by +++, it has also a central symmetry w.r.t the point indicated by #. . Triangle begins: 1; 4, 6; 9, 36, 44; 16, 120, 192, 276; 25, 300, 596, 1130, 2010; 36, 630, 1436, 3321, 6880, 16400; 49, 1176, 3024, 8272, 20600, 57564, 120940; 64, 2016, 5568, 17528, 49184, 159784, 380344, 1075344; CROSSREFS Cf. A090642, A098485, A098487, A291716, A291717, A292152, A292153, A292154, A292155, A292156. Sequence in context: A227553 A108270 A019161 * A137026 A090938 A058229 Adjacent sequences: A291715 A291716 A291717 * A291719 A291720 A291721 KEYWORD nonn,tabl,more AUTHOR Hugo Pfoertner, Sep 08 2017 STATUS approved

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Last modified July 22 00:03 EDT 2024. Contains 374478 sequences. (Running on oeis4.)